{"id":116,"date":"2018-11-08T08:52:50","date_gmt":"2018-11-08T08:52:50","guid":{"rendered":"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=116"},"modified":"2019-04-29T09:20:49","modified_gmt":"2019-04-29T09:20:49","slug":"nuclear-force-and-its-properties-2","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/chapter\/nuclear-force-and-its-properties-2\/","title":{"rendered":"Nuclear Force and its Properties-2"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/6cWqLd365y4\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0 Learning Outcomes<\/strong>\r\n\r\n&nbsp;\r\n\r\nFrom this module students may get to know about the following:\r\n<ul>\r\n \t<li>The knowledge of ground state properties of deuteron.<\/li>\r\n \t<li>The composition of the ground state of deuteron.<\/li>\r\n \t<li>The various components of nuclear force.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0 1.1.3. Spin and parity of deuteron<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The deuteron has non-zero ground state spin. The total spin of deuteron (or in general for a nucleus) is given by<\/p>\r\n<p style=\"text-align: center\"><strong><em>I <\/em><\/strong><strong>= S<\/strong><strong>n<\/strong><strong>+S<\/strong><strong>p<\/strong> <strong>+<em> l<\/em><\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">As the neutron and proton spins can be either parallel or antiparallel, there are four ways to get the total spin as 1 \u0127:<\/p>\r\n&nbsp;\r\n\r\n(a)\u00a0\u00a0 Both neutron and proton spins are up, i.e. <strong>S<\/strong>n and <strong>S<\/strong>p parallel with <strong><em>l<\/em><\/strong> = 0\r\n\r\n(b)\u00a0\u00a0\u00a0 Neutron and proton spins are antiparallel, i.e.\u00a0 <strong>S<\/strong>n and <strong>S<\/strong>p antiparallel with <strong><em>l<\/em><\/strong> = 1\r\n\r\n(c)\u00a0\u00a0 Both neutron and proton spins are parallel, i.e.\u00a0 <strong>S<\/strong>n and <strong>S<\/strong>p parallel with <strong><em>l<\/em><\/strong> = 1\r\n\r\n(d)\u00a0\u00a0\u00a0 Both neutron and proton spins are parallel, i.e. <strong>S<\/strong>n and <strong>S<\/strong>p parallel with <strong><em>l<\/em><\/strong> = 2\r\n\r\n<\/div>\r\n<img class=\"wp-image-120 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-59.png\" alt=\"\" width=\"476\" height=\"154\" \/>\r\n<div>\r\n<p style=\"text-align: center\"><strong>Fig. 1: <\/strong>Parallel and antiparallel combination of neutron and proton.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Since the experimentally measured parity of deuteron is even so only l = 0 and l = 2 give the correct parity determined from experimental observations. It implies that two nucleons are not bound together if their spins are anti-parallel. Since the parallel spin state is forbidden by the Pauli Exclusion Principle in case of identical particles so there are no proton-proton or neutron-neutron bound states. Thus the nuclear force is spin dependent.<\/p>\r\n&nbsp;\r\n\r\n<strong>Magnetic dipole moment of deuteron:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">If <em>l<\/em> = 0 is perfect description for deuteron, there should be no orbital contribution to the magnetic moment. Thus the total magnetic moment of deuteron will be the combination of the neutron and proton magnetic moments:<\/p>\r\n<img class=\"wp-image-121 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-60.png\" alt=\"\" width=\"746\" height=\"53\" \/>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Where g<\/span><em style=\"text-align: initial;font-size: 1em\">s<\/em><span style=\"text-align: initial;font-size: 1em\">n = -3.826084 &amp; g<\/span><em style=\"text-align: initial;font-size: 1em\">s<\/em><span style=\"text-align: initial;font-size: 1em\">p = 5.585691 are the spin g-factor experimentally, = z when spins have their maximum value (\u045b), so<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"wp-image-122 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-61.png\" alt=\"\" width=\"745\" height=\"50\" \/>\r\n\r\n<\/div>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The observed value of \u03bc is 0.8574376 \u00b1 0.0000004 \u03bcN. The Observed value is very close but not in exact agreement with the calculated value. The disagreement between the measured and the calculated values can be due to variet of reasons like:<\/span><\/p>\r\n\r\n<ul>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Modifications in the internal structure of proton and neutron in the bound state so that gsp &amp; gsn get different than their free values. Which is extremely unlikely, as deuteron is only a loosely bound system.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">There are contributions from charged (virtual) mesons exchanged between the proton and the neutron, and these have not been included. It is possible as in fact it has been shown that measonic currents are important in understanding magnetic dipole moments of odd-mass nuclei.<\/li>\r\n \t<li style=\"text-align: justify\">There is a small admixture of the 3D1-state in deuteron ground state.<\/li>\r\n<\/ul>\r\n<div>\r\n<p style=\"text-align: justify\">As the experimental value of magnetic dipole moment of Deuteron, is very close to the calculated value, so admixture (if any) must be very small.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"alignnone wp-image-123 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-62.png\" alt=\"\" width=\"746\" height=\"271\" \/>\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Electric quadrupole moment of deuteron:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">For bare neutron &amp; proton the electric quadrupole moment is zero (Q = 0), so any measured nonzero value of Q must be due to the orbital motion. The observed value of electric quadrupole moment is<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"wp-image-125 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-63.png\" alt=\"\" width=\"747\" height=\"32\" \/>\r\n<p style=\"text-align: justify\">The quadrupole moment of a nuclear state is defined <strong>as<\/strong> the expectation value of <strong><em>Q<\/em><\/strong><strong><em>o<\/em><\/strong> in the substate of maximum <em>M.<\/em> i.e.,<\/p>\r\n<img class=\"wp-image-126 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-64.png\" alt=\"\" width=\"745\" height=\"35\" \/>\r\n\r\n<\/div>\r\n<div>\r\n<p style=\"text-align: justify\">As for any nuclear state with <em>J<\/em> &lt; <strong>1,<\/strong> Q0 = 0. So observation of non-zero quadrupole moment in deuteron implies that <strong><em>L&gt;1 (<\/em><\/strong>direct evidence <em>of<\/em> 3D1-component) in deuteron ground state. Thus the mixing of <em>l<\/em> values is the deuteron is a direct proof of non-central (tensor) term in nuclear interaction<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">In calculating Q0, the biggest challenge is to get a proper d-state wave function. Calculations using d-state wave function obtained from realistic phenomenological potential suggest a few percent mix of d-state wave function in the ground state of deuteron.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Scattering experiments using deuterons as targets give d-state admixtures ~ 4%. This validates our conclusions drawn from the values of and Q.<\/p>\r\n&nbsp;\r\n\r\n<strong>2. Nuclear interaction potential :<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">From the study of the properties of deuteron, it can be concluded that the nuclear interaction unlike other interactions is a complicated function of various terms;<\/p>\r\n&nbsp;\r\n\r\n<strong>1<\/strong><strong>st<\/strong><strong> term: <\/strong>central component (dominant term, VC(r))\r\n\r\n&nbsp;\r\n\r\nIt doesn\u2019t dependent on and\u00a0\u00a0 and can be written as VC(r).\r\n\r\n&nbsp;\r\n\r\n<strong>2<\/strong><strong>nd<\/strong><strong> term: <\/strong>Spin term (a function of<strong> s<\/strong><strong>1<\/strong><strong>, s<\/strong><strong>2<\/strong><strong>)<\/strong>\r\n\r\n&nbsp;\r\n\r\nThere are two orientations of spins for each nucleon. Arrows up (\u2191) and arrows down (\u2193) are used to denote spin orientations.\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Symmetric spin wave functions for a two nucleon system are<\/p>\r\n<img class=\"alignnone wp-image-127 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-65.png\" alt=\"\" width=\"749\" height=\"150\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The above three wave functions correspond to three magnetic substates, M = 1, -1, 0, respectively, of the spin S = 1 state resulting from the coupling of two spin 1\/2 particles. Spin S = 1 coupling is referred to as the triplet.<\/p>\r\n&nbsp;\r\n\r\nThere is only one antisymmetric spin function for a two nucleon system:\r\n\r\n<img class=\"alignnone wp-image-130 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-66.png\" alt=\"\" width=\"750\" height=\"545\" \/>\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">\u00a0<img class=\"alignnone wp-image-131 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-67.png\" alt=\"\" width=\"739\" height=\"295\" \/><\/strong>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 <\/strong><span style=\"text-decoration: underline\"><strong>3<\/strong><strong>rd<\/strong><\/span><strong style=\"text-align: initial;font-size: 1em\"><span style=\"text-decoration: underline\"> term:<\/span> <\/strong><span style=\"text-align: initial;font-size: 1em\">Nuclear interaction has a non-central (Tensor) component<\/span>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Deuteron has a non-zero electric quadrupole moment which means it is not a pure <\/span><em style=\"text-align: initial;font-size: 1em\">l<\/em><span style=\"text-align: initial;font-size: 1em\"> = 0 state but also a small admixture of the <\/span><em style=\"text-align: initial;font-size: 1em\">l<\/em><span style=\"text-align: initial;font-size: 1em\"> = 2 state. So, there is a non-central, \u2018Tensor\u2019 component. Thus the term must be of the form V(r) rather V (r). Tensor force between nucleons in the nucleus provides a more definite description of the average potential experienced by nucleons and the effective residual interaction between them.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">As for a nucleon the only reference direction is its spin, so only terms like <\/span><strong style=\"text-align: initial;font-size: 1em\">s . r<\/strong><span style=\"text-align: initial;font-size: 1em\"> and <\/span><strong style=\"text-align: initial;font-size: 1em\">s x r<\/strong><span style=\"text-align: initial;font-size: 1em\">, which relate <\/span><strong style=\"text-align: initial;font-size: 1em\">r<\/strong><span style=\"text-align: initial;font-size: 1em\"> to the direction of <\/span><strong style=\"text-align: initial;font-size: 1em\">s<\/strong><span style=\"text-align: initial;font-size: 1em\"> can contribute. For parity invariance, there must be an even numbers of factors of r potential must have terms like <\/span><strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong> <strong style=\"text-align: initial;font-size: 1em\">. r)(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong> <strong style=\"text-align: initial;font-size: 1em\">. r)<\/strong><span style=\"text-align: initial;font-size: 1em\"> OR <\/span><strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong> <strong style=\"text-align: initial;font-size: 1em\">x r) . (s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong> <strong style=\"text-align: initial;font-size: 1em\">x r)<\/strong><span style=\"text-align: initial;font-size: 1em\">. Where <\/span><strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong> <strong style=\"text-align: initial;font-size: 1em\">x r) .<\/strong> <strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong><strong style=\"text-align: initial;font-size: 1em\"> x r) <\/strong><span style=\"text-align: initial;font-size: 1em\">can be written as<\/span><strong style=\"text-align: initial;font-size: 1em\"> (s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong><strong style=\"text-align: initial;font-size: 1em\"> . r)(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong><strong style=\"text-align: initial;font-size: 1em\"> . r) &amp; (s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong><strong style=\"text-align: initial;font-size: 1em\"> . s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong><strong style=\"text-align: initial;font-size: 1em\">)<\/strong><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"alignnone wp-image-132 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-68.png\" alt=\"\" width=\"743\" height=\"511\" \/>\r\n<p style=\"text-align: justify\"><a href=\"http:\/\/physics.aps.org\/assets\/a94dec0b-dc76-4822-85ce-5f5f80d3e49a\/e2_1.png\"><strong>Fig. 2: <\/strong><\/a>Schematic illustration of the dependence of the sign of the tensor force between two nucleons on the orientation of the spins relative to the spatial coordinates.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The dependence of sign of tensor force between two nucleons in deuteron on the spins orientation relative to the spatial coordinates is shown in figure 2.<\/p>\r\n\r\n<\/div>\r\n<ol start=\"3\">\r\n \t<li><strong> Summary<\/strong><\/li>\r\n<\/ol>\r\n<p style=\"text-align: justify\">The measured properties like the ground state spin and parity, the magnetic dipole moment and the presence of electric quadrupole moment in deuteron suggest that the nuclear interaction is not a simple function, but is a complicated function of various terms. The first and the main contribution in nuclear interaction comes from the \u2018central component\u2019 which has the radial dependence (i.e. Vc (r)). The next important contribution comes from the spin dependent term. The strong interaction also gets significant contribution from other non-central terms like \u2018tensor term\u2019.<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Nuclear Force and its Properties-2<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/6cWqLd365y4\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\"><em>References:<\/em><\/strong><\/p>\r\n\r\n<ol>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Introduction to Nuclear Physics \u2013 by Keneth S Krane.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Introductory Nuclear Physics \u2013 by Samuel S M Wong.<\/li>\r\n \t<li style=\"text-align: justify\">Nuclear Physics \u2013 by R R Roy &amp; B P Nigam.<\/li>\r\n \t<li style=\"text-align: justify\">Handbook of Physics by Condon and Odishaw, TMH NewYork.<\/li>\r\n \t<li style=\"text-align: justify\">Introduction to Nuclear Physics, 2nd Edition, W.N.Cottingham &amp; D.A. Greenwood.<\/li>\r\n \t<li style=\"text-align: justify\">Concept of Nuclear Physics by B L Cohen, McGraw Hill.<\/li>\r\n \t<li style=\"text-align: justify\">Nuclear Physics ; an Introduction by S.B. Patel.<\/li>\r\n \t<li style=\"text-align: justify\">The Origin of the Concept of Nuclear Force by L.M. Brown and Rechenberg.<\/li>\r\n \t<li style=\"text-align: justify\">Theoretical Nuclear Physics by John M. Blatt and Victor F. Weisskopf.<\/li>\r\n \t<li style=\"text-align: justify\">Experimental techniques in Nuclear Physics by Dorin N. Poenaru &amp; Walter Greiner<\/li>\r\n \t<li style=\"text-align: justify\">Exotic Nuclear Excitation by S.C. Pancholi<\/li>\r\n \t<li style=\"text-align: justify\">Nuclear spectroscopy Part B, by Fay Ajzenberg- Selove<\/li>\r\n \t<li style=\"text-align: justify\">Theory and Problems of modern Physics (Schaum\u2019s outline Series)<\/li>\r\n \t<li style=\"text-align: justify\">Basic Ideas &amp; Concepts in Nuclear Physics \u2013 by K Heyde<\/li>\r\n \t<li style=\"text-align: justify\">The \u201cParticles of Modern Physics\u201d by J. D. Stranathan, Philadephia: Blakiston.<\/li>\r\n \t<li style=\"text-align: justify\">5.\u00a0 Nuclear Physics by Irving Kaplan, Narosa Publishing House.<\/li>\r\n<\/ol>\r\n<div>\r\n\r\n<strong><em>\u00a0 \u00a0 Web Links<\/em><\/strong>\r\n<ol>\r\n \t<li><a href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch1.pdf\">http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-<\/a><a href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch1.pdf\">2012\/lecture-notes\/MIT22_02S12_lec_ch1.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/people.nscl.msu.edu\/~lynch\/lecture_wk11.pdf\">https:\/\/people.nscl.msu.edu\/~lynch\/lecture_wk11.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.umich.edu\/~ners311\/CourseLibrary\/bookchapter11.pdf\">http:\/\/www.umich.edu\/~ners311\/CourseLibrary\/bookchapter11.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.jlab.org\/div_dept\/admin\/publications\/papers\/01\/THY01-06.pdf\">https:\/\/www.jlab.org\/div_dept\/admin\/publications\/papers\/01\/THY01-06.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.hep.phy.cam.ac.uk\/~chpotter\/particleandnuclearphysics\/Lecture_03_NuclearForcesAndScattering.pdf\">http:\/\/www.hep.phy.cam.ac.uk\/~chpotter\/particleandnuclearphysics\/Lecture_03_NuclearForcesAndScatt<\/a> <a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.hep.phy.cam.ac.uk\/~chpotter\/particleandnuclearphysics\/Lecture_03_NuclearForcesAndScattering.pdf\">ering.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/freevideolectures.com\/Course\/3343\/Nuclear-Physics-Fundamentals-and-Application\/13\">http:\/\/freevideolectures.com\/Course\/3343\/Nuclear-Physics-Fundamentals-and-Application\/13<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.youtube.com\/watch?v=bdQUOChdafg\">https:\/\/www.youtube.com\/watch?v=bdQUOChdafg<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/rickbradford.co.uk\/CCC9b_SensitivityofDeuteronStabilitytoNuclearForce.pdf\">http:\/\/rickbradford.co.uk\/CCC9b_SensitivityofDeuteronStabilitytoNuclearForce.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.youtube.com\/watch?v=ovHGUsu1NfM\">https:\/\/www.youtube.com\/watch?v=ovHGUsu1NfM<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/en.wikipedia.org\/wiki\/Nuclear_force\">https:\/\/en.wikipedia.org\/wiki\/Nuclear_force<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ac.els-cdn.com\/0029558262904844\/1-s2.0-0029558262904844-main.pdf?_tid=04fc5b22-1f2a-11e6-bf60-00000aacb35f&amp;acdnat=1463817781_9a8b401f8d0536eacd9a2de52b62e0c1\">http:\/\/ac.els-cdn.com\/0029558262904844\/1-s2.0-0029558262904844-main.pdf?_tid=04fc5b22-1f2a-<\/a><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ac.els-cdn.com\/0029558262904844\/1-s2.0-0029558262904844-main.pdf?_tid=04fc5b22-1f2a-11e6-bf60-00000aacb35f&amp;acdnat=1463817781_9a8b401f8d0536eacd9a2de52b62e0c1\">11e6-bf60-00000aacb35f&amp;acdnat=1463817781_9a8b401f8d0536eacd9a2de52b62e0c1<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch5.pdf\">http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-<\/a><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch5.pdf\">2012\/lecture-notes\/MIT22_02S12_lec_ch5.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/link.springer.com\/chapter\/10.1007\/3-540-27844-3_10#page-1\">http:\/\/link.springer.com\/chapter\/10.1007\/3-540-27844-3_10#page-1<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/oregonstate.edu\/instruct\/ch374\/ch418518\/Chapter%205%20Nuclear%20Forces.pdf\">http:\/\/oregonstate.edu\/instruct\/ch374\/ch418518\/Chapter%205%20Nuclear%20Forces.pdf<\/a><\/li>\r\n \t<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.researchgate.net\/publication\/238997897_The_Meson_Theory_of_Nuclear_Forces_I_The_Deuteron_Ground_State_and_Low_Energy_Neutron-Proton_Scattering\">https:\/\/www.researchgate.net\/publication\/238997897_The_Meson_Theory_of_Nuclear_Forces_I_The_<\/a> <a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.researchgate.net\/publication\/238997897_The_Meson_Theory_of_Nuclear_Forces_I_The_Deuteron_Ground_State_and_Low_Energy_Neutron-Proton_Scattering\">Deuteron_Ground_State_and_Low_Energy_Neutron-Proton_Scattering<\/a><\/li>\r\n<\/ol>\r\n<\/div>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0\u00a0<\/strong><strong>Did you know ?<\/strong>\r\n<ol>\r\n \t<li>A deuteron (2H) is a simple nucleus consisting of only a proton and a neutron.<\/li>\r\n \t<li>It is simplest bound state of nucleons and therefore an ideal system to studying the nuclear interaction.<\/li>\r\n \t<li>Deuteron is a weakly bound system and therefore doesn\u2019t have an excited state.<\/li>\r\n \t<li>Since deuteron is an isotope of hydrogen, the proton is in 1s state (L = 0) and therefore in ground state, it has zero orbital angular momentum.<\/li>\r\n \t<li>Since the measured ground state spin of deuteron is 1, so it indicates that the proton and neutron inside the deuteron have parallel spins (<strong>S<\/strong><strong style=\"text-align: initial;font-size: 1em\">n<\/strong><span style=\"text-align: initial;font-size: 1em\"> + <strong>S<\/strong><\/span><strong style=\"text-align: initial;font-size: 1em\">p<\/strong><span style=\"text-align: initial;font-size: 1em\"> = <\/span><strong style=\"text-align: initial;font-size: 1em\">\u00bd + \u00bd<\/strong><span style=\"text-align: initial;font-size: 1em\"> = <\/span><strong style=\"text-align: initial;font-size: 1em\">1<\/strong><span style=\"text-align: initial;font-size: 1em\">).<\/span><\/li>\r\n \t<li>The existence of deuteron with parallel neutron -proton spins justify the non \u2013observation of proton-proton (anti-parallel spins) and neutron \u2013neutron bound systems. The Pauli\u2019s principle forbids the parallel spin state for identical particles and therefore such states will not be stable.<\/li>\r\n \t<li>The observation of a stable deuteron (with parallel spins) and non-observation of a stable 2-proton and 2-neutrons is an indication of spin dependent nature of nuclear force.<\/li>\r\n \t<li>The observation of significant value of ground state quadrupole moment in deuteron confirms that its ground state in non-spherical (1S0) i.e. not a pure S-state.<\/li>\r\n \t<li>The little disagreement of the observed value from the predicted value of magnetic moment in Deuteron indicates that its ground state is a mixed state, i.e. a combination of a S-state and a D-state.<\/li>\r\n \t<li>The S = 1 state configuration has the lowest energy, so the nuclear force must be more attractive for total spin S = 1 (parallel spin) than for S = 0 (anti-parallel spin).<\/li>\r\n \t<li>The observed hole in the center of deuteron nucleus means that at very short distances, the nuclear force is repulsive i.e. the neutron and the proton wave functions do not overlap.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<strong><em>\u00a0 \u00a0 Biography:<\/em><\/strong>\r\n<ol>\r\n \t<li><a style=\"font-size: 1em\" href=\"https:\/\/en.wikipedia.org\/wiki\/Hans_Bethe\">https:\/\/en.wikipedia.org\/wiki\/Hans_Bethe<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www-history.mcs.st-and.ac.uk\/Biographies\/Bethe.html\">http:\/\/www-history.mcs.st-and.ac.uk\/Biographies\/Bethe.html<\/a><\/li>\r\n \t<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hideki_Yukawa\">https:\/\/en.wikipedia.org\/wiki\/Hideki_Yukawa<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1949\/yukawa-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1949\/yukawa-bio.html<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.encyclopedia.com\/topic\/Hideki_Yukawa.aspx\">http:\/\/www.encyclopedia.com\/topic\/Hideki_Yukawa.aspx<\/a><\/li>\r\n \t<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Peter_Higgs\">https:\/\/en.wikipedia.org\/wiki\/Peter_Higgs<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.ph.ed.ac.uk\/higgs\/peter-higgs\">http:\/\/www.ph.ed.ac.uk\/higgs\/peter-higgs<\/a><\/li>\r\n \t<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Paul_Dirac\">https:\/\/en.wikipedia.org\/wiki\/Paul_Dirac<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/dirac-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/dirac-bio.html<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www-groups.dcs.st-and.ac.uk\/~history\/Biographies\/Dirac.html\">http:\/\/www-groups.dcs.st-and.ac.uk\/~history\/Biographies\/Dirac.html<\/a><\/li>\r\n \t<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Erwin_Schr%C3%B6dinger\">https:\/\/en.wikipedia.org\/wiki\/Erwin_Schr%C3%B6dinger<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/schrodinger-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/schrodinger-bio.html<\/a><\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/6cWqLd365y4\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<div>\n<p><strong>\u00a0 \u00a0 Learning Outcomes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>From this module students may get to know about the following:<\/p>\n<ul>\n<li>The knowledge of ground state properties of deuteron.<\/li>\n<li>The composition of the ground state of deuteron.<\/li>\n<li>The various components of nuclear force.<\/li>\n<\/ul>\n<\/div>\n<div>\n<p><strong>\u00a0 \u00a0 1.1.3. Spin and parity of deuteron<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The deuteron has non-zero ground state spin. The total spin of deuteron (or in general for a nucleus) is given by<\/p>\n<p style=\"text-align: center\"><strong><em>I <\/em><\/strong><strong>= S<\/strong><strong>n<\/strong><strong>+S<\/strong><strong>p<\/strong> <strong>+<em> l<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">As the neutron and proton spins can be either parallel or antiparallel, there are four ways to get the total spin as 1 \u0127:<\/p>\n<p>&nbsp;<\/p>\n<p>(a)\u00a0\u00a0 Both neutron and proton spins are up, i.e. <strong>S<\/strong>n and <strong>S<\/strong>p parallel with <strong><em>l<\/em><\/strong> = 0<\/p>\n<p>(b)\u00a0\u00a0\u00a0 Neutron and proton spins are antiparallel, i.e.\u00a0 <strong>S<\/strong>n and <strong>S<\/strong>p antiparallel with <strong><em>l<\/em><\/strong> = 1<\/p>\n<p>(c)\u00a0\u00a0 Both neutron and proton spins are parallel, i.e.\u00a0 <strong>S<\/strong>n and <strong>S<\/strong>p parallel with <strong><em>l<\/em><\/strong> = 1<\/p>\n<p>(d)\u00a0\u00a0\u00a0 Both neutron and proton spins are parallel, i.e. <strong>S<\/strong>n and <strong>S<\/strong>p parallel with <strong><em>l<\/em><\/strong> = 2<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-120 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-59.png\" alt=\"\" width=\"476\" height=\"154\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-59.png 476w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-59-300x97.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-59-65x21.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-59-225x73.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-59-350x113.png 350w\" sizes=\"auto, (max-width: 476px) 100vw, 476px\" \/><\/p>\n<div>\n<p style=\"text-align: center\"><strong>Fig. 1: <\/strong>Parallel and antiparallel combination of neutron and proton.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Since the experimentally measured parity of deuteron is even so only l = 0 and l = 2 give the correct parity determined from experimental observations. It implies that two nucleons are not bound together if their spins are anti-parallel. Since the parallel spin state is forbidden by the Pauli Exclusion Principle in case of identical particles so there are no proton-proton or neutron-neutron bound states. Thus the nuclear force is spin dependent.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Magnetic dipole moment of deuteron:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">If <em>l<\/em> = 0 is perfect description for deuteron, there should be no orbital contribution to the magnetic moment. Thus the total magnetic moment of deuteron will be the combination of the neutron and proton magnetic moments:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-121 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-60.png\" alt=\"\" width=\"746\" height=\"53\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-60.png 746w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-60-300x21.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-60-65x5.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-60-225x16.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-60-350x25.png 350w\" sizes=\"auto, (max-width: 746px) 100vw, 746px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Where g<\/span><em style=\"text-align: initial;font-size: 1em\">s<\/em><span style=\"text-align: initial;font-size: 1em\">n = -3.826084 &amp; g<\/span><em style=\"text-align: initial;font-size: 1em\">s<\/em><span style=\"text-align: initial;font-size: 1em\">p = 5.585691 are the spin g-factor experimentally, = z when spins have their maximum value (\u045b), so<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-122 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-61.png\" alt=\"\" width=\"745\" height=\"50\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-61.png 745w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-61-300x20.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-61-65x4.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-61-225x15.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-61-350x23.png 350w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/p>\n<\/div>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The observed value of \u03bc is 0.8574376 \u00b1 0.0000004 \u03bcN. The Observed value is very close but not in exact agreement with the calculated value. The disagreement between the measured and the calculated values can be due to variet of reasons like:<\/span><\/p>\n<ul>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Modifications in the internal structure of proton and neutron in the bound state so that gsp &amp; gsn get different than their free values. Which is extremely unlikely, as deuteron is only a loosely bound system.<\/span><\/li>\n<li style=\"text-align: justify\">There are contributions from charged (virtual) mesons exchanged between the proton and the neutron, and these have not been included. It is possible as in fact it has been shown that measonic currents are important in understanding magnetic dipole moments of odd-mass nuclei.<\/li>\n<li style=\"text-align: justify\">There is a small admixture of the 3D1-state in deuteron ground state.<\/li>\n<\/ul>\n<div>\n<p style=\"text-align: justify\">As the experimental value of magnetic dipole moment of Deuteron, is very close to the calculated value, so admixture (if any) must be very small.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-123 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-62.png\" alt=\"\" width=\"746\" height=\"271\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-62.png 746w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-62-300x109.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-62-65x24.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-62-225x82.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-62-350x127.png 350w\" sizes=\"auto, (max-width: 746px) 100vw, 746px\" \/><\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Electric quadrupole moment of deuteron:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">For bare neutron &amp; proton the electric quadrupole moment is zero (Q = 0), so any measured nonzero value of Q must be due to the orbital motion. The observed value of electric quadrupole moment is<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-125 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-63.png\" alt=\"\" width=\"747\" height=\"32\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-63.png 747w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-63-300x13.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-63-65x3.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-63-225x10.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-63-350x15.png 350w\" sizes=\"auto, (max-width: 747px) 100vw, 747px\" \/><\/p>\n<p style=\"text-align: justify\">The quadrupole moment of a nuclear state is defined <strong>as<\/strong> the expectation value of <strong><em>Q<\/em><\/strong><strong><em>o<\/em><\/strong> in the substate of maximum <em>M.<\/em> i.e.,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-126 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-64.png\" alt=\"\" width=\"745\" height=\"35\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-64.png 745w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-64-300x14.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-64-65x3.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-64-225x11.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-64-350x16.png 350w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/p>\n<\/div>\n<div>\n<p style=\"text-align: justify\">As for any nuclear state with <em>J<\/em> &lt; <strong>1,<\/strong> Q0 = 0. So observation of non-zero quadrupole moment in deuteron implies that <strong><em>L&gt;1 (<\/em><\/strong>direct evidence <em>of<\/em> 3D1-component) in deuteron ground state. Thus the mixing of <em>l<\/em> values is the deuteron is a direct proof of non-central (tensor) term in nuclear interaction<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In calculating Q0, the biggest challenge is to get a proper d-state wave function. Calculations using d-state wave function obtained from realistic phenomenological potential suggest a few percent mix of d-state wave function in the ground state of deuteron.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Scattering experiments using deuterons as targets give d-state admixtures ~ 4%. This validates our conclusions drawn from the values of and Q.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>2. Nuclear interaction potential :<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">From the study of the properties of deuteron, it can be concluded that the nuclear interaction unlike other interactions is a complicated function of various terms;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>1<\/strong><strong>st<\/strong><strong> term: <\/strong>central component (dominant term, VC(r))<\/p>\n<p>&nbsp;<\/p>\n<p>It doesn\u2019t dependent on and\u00a0\u00a0 and can be written as VC(r).<\/p>\n<p>&nbsp;<\/p>\n<p><strong>2<\/strong><strong>nd<\/strong><strong> term: <\/strong>Spin term (a function of<strong> s<\/strong><strong>1<\/strong><strong>, s<\/strong><strong>2<\/strong><strong>)<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>There are two orientations of spins for each nucleon. Arrows up (\u2191) and arrows down (\u2193) are used to denote spin orientations.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Symmetric spin wave functions for a two nucleon system are<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-127 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-65.png\" alt=\"\" width=\"749\" height=\"150\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-65.png 749w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-65-300x60.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-65-65x13.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-65-225x45.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-65-350x70.png 350w\" sizes=\"auto, (max-width: 749px) 100vw, 749px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The above three wave functions correspond to three magnetic substates, M = 1, -1, 0, respectively, of the spin S = 1 state resulting from the coupling of two spin 1\/2 particles. Spin S = 1 coupling is referred to as the triplet.<\/p>\n<p>&nbsp;<\/p>\n<p>There is only one antisymmetric spin function for a two nucleon system:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-130 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-66.png\" alt=\"\" width=\"750\" height=\"545\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-66.png 750w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-66-300x218.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-66-65x47.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-66-225x164.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-66-350x254.png 350w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-131 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-67.png\" alt=\"\" width=\"739\" height=\"295\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-67.png 739w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-67-300x120.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-67-65x26.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-67-225x90.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-67-350x140.png 350w\" sizes=\"auto, (max-width: 739px) 100vw, 739px\" \/><\/strong><\/p>\n<\/div>\n<div>\n<p><strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 <\/strong><span style=\"text-decoration: underline\"><strong>3<\/strong><strong>rd<\/strong><\/span><strong style=\"text-align: initial;font-size: 1em\"><span style=\"text-decoration: underline\"> term:<\/span> <\/strong><span style=\"text-align: initial;font-size: 1em\">Nuclear interaction has a non-central (Tensor) component<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Deuteron has a non-zero electric quadrupole moment which means it is not a pure <\/span><em style=\"text-align: initial;font-size: 1em\">l<\/em><span style=\"text-align: initial;font-size: 1em\"> = 0 state but also a small admixture of the <\/span><em style=\"text-align: initial;font-size: 1em\">l<\/em><span style=\"text-align: initial;font-size: 1em\"> = 2 state. So, there is a non-central, \u2018Tensor\u2019 component. Thus the term must be of the form V(r) rather V (r). Tensor force between nucleons in the nucleus provides a more definite description of the average potential experienced by nucleons and the effective residual interaction between them.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">As for a nucleon the only reference direction is its spin, so only terms like <\/span><strong style=\"text-align: initial;font-size: 1em\">s . r<\/strong><span style=\"text-align: initial;font-size: 1em\"> and <\/span><strong style=\"text-align: initial;font-size: 1em\">s x r<\/strong><span style=\"text-align: initial;font-size: 1em\">, which relate <\/span><strong style=\"text-align: initial;font-size: 1em\">r<\/strong><span style=\"text-align: initial;font-size: 1em\"> to the direction of <\/span><strong style=\"text-align: initial;font-size: 1em\">s<\/strong><span style=\"text-align: initial;font-size: 1em\"> can contribute. For parity invariance, there must be an even numbers of factors of r potential must have terms like <\/span><strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong> <strong style=\"text-align: initial;font-size: 1em\">. r)(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong> <strong style=\"text-align: initial;font-size: 1em\">. r)<\/strong><span style=\"text-align: initial;font-size: 1em\"> OR <\/span><strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong> <strong style=\"text-align: initial;font-size: 1em\">x r) . (s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong> <strong style=\"text-align: initial;font-size: 1em\">x r)<\/strong><span style=\"text-align: initial;font-size: 1em\">. Where <\/span><strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong> <strong style=\"text-align: initial;font-size: 1em\">x r) .<\/strong> <strong style=\"text-align: initial;font-size: 1em\">(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong><strong style=\"text-align: initial;font-size: 1em\"> x r) <\/strong><span style=\"text-align: initial;font-size: 1em\">can be written as<\/span><strong style=\"text-align: initial;font-size: 1em\"> (s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong><strong style=\"text-align: initial;font-size: 1em\"> . r)(s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong><strong style=\"text-align: initial;font-size: 1em\"> . r) &amp; (s<\/strong><strong style=\"text-align: initial;font-size: 1em\">1<\/strong><strong style=\"text-align: initial;font-size: 1em\"> . s<\/strong><strong style=\"text-align: initial;font-size: 1em\">2<\/strong><strong style=\"text-align: initial;font-size: 1em\">)<\/strong><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-132 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-68.png\" alt=\"\" width=\"743\" height=\"511\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-68.png 743w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-68-300x206.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-68-65x45.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-68-225x155.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-68-350x241.png 350w\" sizes=\"auto, (max-width: 743px) 100vw, 743px\" \/><\/p>\n<p style=\"text-align: justify\"><a href=\"http:\/\/physics.aps.org\/assets\/a94dec0b-dc76-4822-85ce-5f5f80d3e49a\/e2_1.png\"><strong>Fig. 2: <\/strong><\/a>Schematic illustration of the dependence of the sign of the tensor force between two nucleons on the orientation of the spins relative to the spatial coordinates.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The dependence of sign of tensor force between two nucleons in deuteron on the spins orientation relative to the spatial coordinates is shown in figure 2.<\/p>\n<\/div>\n<ol start=\"3\">\n<li><strong> Summary<\/strong><\/li>\n<\/ol>\n<p style=\"text-align: justify\">The measured properties like the ground state spin and parity, the magnetic dipole moment and the presence of electric quadrupole moment in deuteron suggest that the nuclear interaction is not a simple function, but is a complicated function of various terms. The first and the main contribution in nuclear interaction comes from the \u2018central component\u2019 which has the radial dependence (i.e. Vc (r)). The next important contribution comes from the spin dependent term. The strong interaction also gets significant contribution from other non-central terms like \u2018tensor term\u2019.<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Nuclear Force and its Properties-2<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/6cWqLd365y4\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\"><em>References:<\/em><\/strong><\/p>\n<ol>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Introduction to Nuclear Physics \u2013 by Keneth S Krane.<\/span><\/li>\n<li style=\"text-align: justify\">Introductory Nuclear Physics \u2013 by Samuel S M Wong.<\/li>\n<li style=\"text-align: justify\">Nuclear Physics \u2013 by R R Roy &amp; B P Nigam.<\/li>\n<li style=\"text-align: justify\">Handbook of Physics by Condon and Odishaw, TMH NewYork.<\/li>\n<li style=\"text-align: justify\">Introduction to Nuclear Physics, 2nd Edition, W.N.Cottingham &amp; D.A. Greenwood.<\/li>\n<li style=\"text-align: justify\">Concept of Nuclear Physics by B L Cohen, McGraw Hill.<\/li>\n<li style=\"text-align: justify\">Nuclear Physics ; an Introduction by S.B. Patel.<\/li>\n<li style=\"text-align: justify\">The Origin of the Concept of Nuclear Force by L.M. Brown and Rechenberg.<\/li>\n<li style=\"text-align: justify\">Theoretical Nuclear Physics by John M. Blatt and Victor F. Weisskopf.<\/li>\n<li style=\"text-align: justify\">Experimental techniques in Nuclear Physics by Dorin N. Poenaru &amp; Walter Greiner<\/li>\n<li style=\"text-align: justify\">Exotic Nuclear Excitation by S.C. Pancholi<\/li>\n<li style=\"text-align: justify\">Nuclear spectroscopy Part B, by Fay Ajzenberg- Selove<\/li>\n<li style=\"text-align: justify\">Theory and Problems of modern Physics (Schaum\u2019s outline Series)<\/li>\n<li style=\"text-align: justify\">Basic Ideas &amp; Concepts in Nuclear Physics \u2013 by K Heyde<\/li>\n<li style=\"text-align: justify\">The \u201cParticles of Modern Physics\u201d by J. D. Stranathan, Philadephia: Blakiston.<\/li>\n<li style=\"text-align: justify\">5.\u00a0 Nuclear Physics by Irving Kaplan, Narosa Publishing House.<\/li>\n<\/ol>\n<div>\n<p><strong><em>\u00a0 \u00a0 Web Links<\/em><\/strong><\/p>\n<ol>\n<li><a href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch1.pdf\">http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-<\/a><a href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch1.pdf\">2012\/lecture-notes\/MIT22_02S12_lec_ch1.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/people.nscl.msu.edu\/~lynch\/lecture_wk11.pdf\">https:\/\/people.nscl.msu.edu\/~lynch\/lecture_wk11.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.umich.edu\/~ners311\/CourseLibrary\/bookchapter11.pdf\">http:\/\/www.umich.edu\/~ners311\/CourseLibrary\/bookchapter11.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.jlab.org\/div_dept\/admin\/publications\/papers\/01\/THY01-06.pdf\">https:\/\/www.jlab.org\/div_dept\/admin\/publications\/papers\/01\/THY01-06.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.hep.phy.cam.ac.uk\/~chpotter\/particleandnuclearphysics\/Lecture_03_NuclearForcesAndScattering.pdf\">http:\/\/www.hep.phy.cam.ac.uk\/~chpotter\/particleandnuclearphysics\/Lecture_03_NuclearForcesAndScatt<\/a> <a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.hep.phy.cam.ac.uk\/~chpotter\/particleandnuclearphysics\/Lecture_03_NuclearForcesAndScattering.pdf\">ering.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/freevideolectures.com\/Course\/3343\/Nuclear-Physics-Fundamentals-and-Application\/13\">http:\/\/freevideolectures.com\/Course\/3343\/Nuclear-Physics-Fundamentals-and-Application\/13<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.youtube.com\/watch?v=bdQUOChdafg\">https:\/\/www.youtube.com\/watch?v=bdQUOChdafg<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/rickbradford.co.uk\/CCC9b_SensitivityofDeuteronStabilitytoNuclearForce.pdf\">http:\/\/rickbradford.co.uk\/CCC9b_SensitivityofDeuteronStabilitytoNuclearForce.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.youtube.com\/watch?v=ovHGUsu1NfM\">https:\/\/www.youtube.com\/watch?v=ovHGUsu1NfM<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/en.wikipedia.org\/wiki\/Nuclear_force\">https:\/\/en.wikipedia.org\/wiki\/Nuclear_force<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ac.els-cdn.com\/0029558262904844\/1-s2.0-0029558262904844-main.pdf?_tid=04fc5b22-1f2a-11e6-bf60-00000aacb35f&amp;acdnat=1463817781_9a8b401f8d0536eacd9a2de52b62e0c1\">http:\/\/ac.els-cdn.com\/0029558262904844\/1-s2.0-0029558262904844-main.pdf?_tid=04fc5b22-1f2a-<\/a><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ac.els-cdn.com\/0029558262904844\/1-s2.0-0029558262904844-main.pdf?_tid=04fc5b22-1f2a-11e6-bf60-00000aacb35f&amp;acdnat=1463817781_9a8b401f8d0536eacd9a2de52b62e0c1\">11e6-bf60-00000aacb35f&amp;acdnat=1463817781_9a8b401f8d0536eacd9a2de52b62e0c1<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch5.pdf\">http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-<\/a><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/ocw.mit.edu\/courses\/nuclear-engineering\/22-02-introduction-to-applied-nuclear-physics-spring-2012\/lecture-notes\/MIT22_02S12_lec_ch5.pdf\">2012\/lecture-notes\/MIT22_02S12_lec_ch5.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/link.springer.com\/chapter\/10.1007\/3-540-27844-3_10#page-1\">http:\/\/link.springer.com\/chapter\/10.1007\/3-540-27844-3_10#page-1<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/oregonstate.edu\/instruct\/ch374\/ch418518\/Chapter%205%20Nuclear%20Forces.pdf\">http:\/\/oregonstate.edu\/instruct\/ch374\/ch418518\/Chapter%205%20Nuclear%20Forces.pdf<\/a><\/li>\n<li><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.researchgate.net\/publication\/238997897_The_Meson_Theory_of_Nuclear_Forces_I_The_Deuteron_Ground_State_and_Low_Energy_Neutron-Proton_Scattering\">https:\/\/www.researchgate.net\/publication\/238997897_The_Meson_Theory_of_Nuclear_Forces_I_The_<\/a> <a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/www.researchgate.net\/publication\/238997897_The_Meson_Theory_of_Nuclear_Forces_I_The_Deuteron_Ground_State_and_Low_Energy_Neutron-Proton_Scattering\">Deuteron_Ground_State_and_Low_Energy_Neutron-Proton_Scattering<\/a><\/li>\n<\/ol>\n<\/div>\n<div>\n<p><strong>\u00a0 \u00a0\u00a0<\/strong><strong>Did you know ?<\/strong><\/p>\n<ol>\n<li>A deuteron (2H) is a simple nucleus consisting of only a proton and a neutron.<\/li>\n<li>It is simplest bound state of nucleons and therefore an ideal system to studying the nuclear interaction.<\/li>\n<li>Deuteron is a weakly bound system and therefore doesn\u2019t have an excited state.<\/li>\n<li>Since deuteron is an isotope of hydrogen, the proton is in 1s state (L = 0) and therefore in ground state, it has zero orbital angular momentum.<\/li>\n<li>Since the measured ground state spin of deuteron is 1, so it indicates that the proton and neutron inside the deuteron have parallel spins (<strong>S<\/strong><strong style=\"text-align: initial;font-size: 1em\">n<\/strong><span style=\"text-align: initial;font-size: 1em\"> + <strong>S<\/strong><\/span><strong style=\"text-align: initial;font-size: 1em\">p<\/strong><span style=\"text-align: initial;font-size: 1em\"> = <\/span><strong style=\"text-align: initial;font-size: 1em\">\u00bd + \u00bd<\/strong><span style=\"text-align: initial;font-size: 1em\"> = <\/span><strong style=\"text-align: initial;font-size: 1em\">1<\/strong><span style=\"text-align: initial;font-size: 1em\">).<\/span><\/li>\n<li>The existence of deuteron with parallel neutron -proton spins justify the non \u2013observation of proton-proton (anti-parallel spins) and neutron \u2013neutron bound systems. The Pauli\u2019s principle forbids the parallel spin state for identical particles and therefore such states will not be stable.<\/li>\n<li>The observation of a stable deuteron (with parallel spins) and non-observation of a stable 2-proton and 2-neutrons is an indication of spin dependent nature of nuclear force.<\/li>\n<li>The observation of significant value of ground state quadrupole moment in deuteron confirms that its ground state in non-spherical (1S0) i.e. not a pure S-state.<\/li>\n<li>The little disagreement of the observed value from the predicted value of magnetic moment in Deuteron indicates that its ground state is a mixed state, i.e. a combination of a S-state and a D-state.<\/li>\n<li>The S = 1 state configuration has the lowest energy, so the nuclear force must be more attractive for total spin S = 1 (parallel spin) than for S = 0 (anti-parallel spin).<\/li>\n<li>The observed hole in the center of deuteron nucleus means that at very short distances, the nuclear force is repulsive i.e. the neutron and the proton wave functions do not overlap.<\/li>\n<\/ol>\n<\/div>\n<p><strong><em>\u00a0 \u00a0 Biography:<\/em><\/strong><\/p>\n<ol>\n<li><a style=\"font-size: 1em\" href=\"https:\/\/en.wikipedia.org\/wiki\/Hans_Bethe\">https:\/\/en.wikipedia.org\/wiki\/Hans_Bethe<\/a><\/li>\n<li><a href=\"http:\/\/www-history.mcs.st-and.ac.uk\/Biographies\/Bethe.html\">http:\/\/www-history.mcs.st-and.ac.uk\/Biographies\/Bethe.html<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hideki_Yukawa\">https:\/\/en.wikipedia.org\/wiki\/Hideki_Yukawa<\/a><\/li>\n<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1949\/yukawa-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1949\/yukawa-bio.html<\/a><\/li>\n<li><a href=\"http:\/\/www.encyclopedia.com\/topic\/Hideki_Yukawa.aspx\">http:\/\/www.encyclopedia.com\/topic\/Hideki_Yukawa.aspx<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Peter_Higgs\">https:\/\/en.wikipedia.org\/wiki\/Peter_Higgs<\/a><\/li>\n<li><a href=\"http:\/\/www.ph.ed.ac.uk\/higgs\/peter-higgs\">http:\/\/www.ph.ed.ac.uk\/higgs\/peter-higgs<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Paul_Dirac\">https:\/\/en.wikipedia.org\/wiki\/Paul_Dirac<\/a><\/li>\n<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/dirac-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/dirac-bio.html<\/a><\/li>\n<li><a href=\"http:\/\/www-groups.dcs.st-and.ac.uk\/~history\/Biographies\/Dirac.html\">http:\/\/www-groups.dcs.st-and.ac.uk\/~history\/Biographies\/Dirac.html<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Erwin_Schr%C3%B6dinger\">https:\/\/en.wikipedia.org\/wiki\/Erwin_Schr%C3%B6dinger<\/a><\/li>\n<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/schrodinger-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/schrodinger-bio.html<\/a><\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":6,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["dr-sanjay-kumar-chamoli"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-116","chapter","type-chapter","status-publish","hentry","contributor-dr-sanjay-kumar-chamoli"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters\/116","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":8,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters\/116\/revisions"}],"predecessor-version":[{"id":341,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters\/116\/revisions\/341"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters\/116\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/media?parent=116"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapter-type?post=116"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/contributor?post=116"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/license?post=116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}