{"id":59,"date":"2018-11-02T10:11:41","date_gmt":"2018-11-02T10:11:41","guid":{"rendered":"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=59"},"modified":"2019-04-29T08:59:55","modified_gmt":"2019-04-29T08:59:55","slug":"basic-nuclear-properties-5","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/chapter\/basic-nuclear-properties-5\/","title":{"rendered":"Basic nuclear properties-5"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/VHx6Tq-mbZk\" 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 basic nuclear properties.<\/li>\r\n \t<li>The importance of nuclear properties.<\/li>\r\n \t<li>The experimental ways of determining nuclear properties.<\/li>\r\n<\/ul>\r\n<strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 1. Spin<\/strong>\r\n<p style=\"text-align: justify\"><img class=\"wp-image-63 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23.png\" alt=\"\" width=\"887\" height=\"133\" \/><\/p>\r\n\r\n<\/div>\r\n<div>\r\n<p style=\"text-align: justify\">\u00a0 1.1. <strong>Directional Correlation Ratio (DCO- ratio)<\/strong> :The information about the DCO ratios is obtained in experiments with multi detector arrays in which the detectors should be placed at different angles with respect to the beam direction. The DCO ratio method is an important tool to infer the spin differences between states observed by the coincidence measurement of the gamma-decay between them.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">1.1.1.\u00a0\u00a0 <strong>Importance of DCO ratio : <\/strong>In comparison to the angular distribution, the DCO ratio is advantages in the sense that<\/p>\r\n-\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 weak transitions can be studied,\r\n\r\n-\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 members of multiplets can be analysed and\r\n\r\n-\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 no normalisation to the beam charge is necessary\r\n\r\n-\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 By use of multidetector arrays the statistical accuracy of the DCO ratios can be increased by analysing many detector combinations .\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">1.1.2 <strong>Calculation of DCO ratio :<\/strong> For most applications the theory of DCO ratios can be simplified with respect to the general directional correlation theory by taking into account the experimental conditions (i) that unpolarized beams are used and (ii) that the detectors are insensitive to the polarization of the -y-rays. Therefore, detectors placed at forward and backward angles with respect to the beam direction can be treated in the same way. The angular correlation of -y-rays emitted from oriented states depends on the spins of the involved levels, the multipolarities and mixing ratios of the -transitions and the m-substate population distribution of the initial state. In the experiment a compound nucleus is produced via fusion evaporation reaction by bombarding a target nucleus with a projectile. The compound nucleus then start decaying by emitting -ray and come to the lower energy state. The -ray from the decaying nucleus are mostly of dipole or quadrupole nature or a mixture of both types. Suppose two detectors 1 and 2, placed at different angles as shown in figure 1, are used to determine the angular correlation of a cascade of two -rays. The detectors are making an angle \u03b81 and \u03b82 with the beam direction. The angle between the planes opened by each detector and the beam axis is.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"wp-image-64 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24.png\" alt=\"\" width=\"889\" height=\"168\" \/>\r\n\r\n<\/div>\r\n<strong>\u00a0<img class=\"alignnone wp-image-65 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25.png\" alt=\"\" width=\"803\" height=\"346\" \/><\/strong>\r\n<div>\r\n<p style=\"text-align: center\"><strong>Fig. 1: <\/strong>Geometry of the detector arrangement with the beam as orientation axis.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"alignnone wp-image-66 \" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-26.png\" alt=\"\" width=\"790\" height=\"552\" \/>\r\n\r\n&nbsp;\r\n\r\n<img class=\"wp-image-68 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-27.png\" alt=\"\" width=\"558\" height=\"333\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong style=\"text-align: initial;font-size: 1em\">Fig. 2: <\/strong><span style=\"text-align: initial;font-size: 1em\">The picture of Indian National Gamma Array (INGA) at TIFR, Mumbai.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"wp-image-69 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-28.png\" alt=\"\" width=\"583\" height=\"382\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Fig. 3: <\/strong>DCO Ratio of the transitions belonging to the band gated by 958 keV transition.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The value of RDCO is approximately unity for quadrupole transition and non stretched dipole, the value between 0.4 and 0.6 for stretched dipole and the value between 0.6 and 0.8 implies a mixed transition.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>1.1.3 Limitations of DCO ratio method : <\/strong>Though the DCO ratio method is advantageous and therefore preferred over angular distribution measurements method, it has its limitation too. The serious disadvantage is that with this method a spin change of I = \u00b1 1 cannot be distinguished.<\/p>\r\n&nbsp;\r\n\r\n<strong>2. Parity<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The parity of a nuclear state can efficiently be determined by measuring the electric and magnetic nature of de-exciting -rays (Linear polarization). The sign of the measured linear polarization\u00a0<span style=\"text-align: initial;font-size: 1em\">distinguishes electric and magnetic types of gamma-ray transitions. Electric transitions have preferential scattering along the perpendicular direction, while magnetic transitions have scattering along parallel direction. Depending on the energy of -ray, Compton scattering, e-- e+ pair production and photoelectric effect can be used for measuring the degree of polarization. The linear polarization along with the angular distribution or DCO ratios measurements can uniquely determine the spins &amp; parities of nuclear states<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2.1 Polarization measurement in nuclei : <\/strong><span style=\"text-align: initial;font-size: 1em\">A conventional Compton polarimeter, used to determine the <\/span>parities<span style=\"text-align: initial;font-size: 1em\"> of different levels in 155Gd is shown in figure 4. It has one scatterer and two absorbers\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">with 25 segments on the front face of a germanium crystal, each of which acts an individual gamma-ray detector. In this polarimeter, there are three planes and four relevant angles to define the linear polarization of the gamma rays.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"wp-image-70 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-29.png\" alt=\"\" width=\"457\" height=\"258\" \/>\r\n\r\nFig. 4: A picture of a conventional Compton polarimeter consisting of one scatterer and two absorbers.\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The linear polarization of gamma rays emitted from oriented states formed in nuclear reactions and the angular distribution of the gamma rays are related to each other. For a linear polarized gamma rays, the angular distribution function depends not on their outgoing direction, \u03b8 with respect to the beam axis and their electric field direction, \u03b5 with respect to the reaction plane. The linear polarization of -rays can be expressed in terms of the angular distribution functions when their electric field is in the reaction plane, W(\u03b8, \u03b5 = 00), and when it is perpendicular to the reaction plane, W(\u03b8, \u03b5 = 90'). i.e;<\/p>\r\n&nbsp;\r\n\r\n<img class=\"wp-image-71 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-30.png\" alt=\"\" width=\"700\" height=\"125\" \/>\r\n\r\n<\/div>\r\n<p style=\"text-align: justify\"><strong>\u00a0<\/strong><strong style=\"text-align: initial;font-size: 1em\">2.2 Calculating polarization coefficients theoretically : <\/strong><span style=\"text-align: initial;font-size: 1em\">The polarization coefficients for pure (electric\/magnetic) dipole and the (electric) quadrupole transitions in terms of angular distribution parameters a2 and a4 can be derived as:<\/span><\/p>\r\n&nbsp;\r\n\r\n<img class=\"wp-image-72 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-31.png\" alt=\"\" width=\"726\" height=\"174\" \/>\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: justify;font-size: 1em\">From the above equations, the maximum value of the polarization in magnitudes at = 90'. Theoretically calculated values of polarization coefficients for pure (electric\/ magnetic) dipole and the (electric) quadrupole transitions are listed in table 1.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<strong>Table 1: <\/strong>Theoretically calculated values of polarization coefficients for pure (electric\/ magnetic) dipole and the (electric) quadrupole transitions.\r\n\r\n<\/div>\r\n<img class=\"wp-image-73 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-32.png\" alt=\"\" width=\"778\" height=\"548\" \/>\r\n\r\n&nbsp;\r\n\r\n<img class=\"wp-image-74 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-33.png\" alt=\"\" width=\"743\" height=\"744\" \/>\r\n<ol start=\"3\">\r\n \t<li style=\"text-align: justify\"><strong>Summary : <\/strong>The spin and parity of important nuclear properties. Knowing the spin and parity of a nuclear eigen state can reveal the underlying single particle configurations involved in the formation of that state. Both, the spin and parity of a nuclear state can be determined experimentally. The spin can be obtained by determining the multipole order and the dipole-quadrupole mixing ratio ( ) of the outgoing gamma radiation. To get the two parameters, measuring DCO ratio is better than the angular distribution, accurate measurements need multi-detector array. The parity of a nuclear state can be obtained by measuring the polarization of outgoing gamma rays. It can be concluded that the investigation of DCO ratios allows the determination of spins and dipole-quadrupole mixing ratios.<\/li>\r\n<\/ol>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Basic nuclear properties-5<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/VHx6Tq-mbZk\" 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\r\n<div>\r\n\r\n<strong><em>\u00a0 \u00a0 \u00a0References:<\/em><\/strong>\r\n<ol>\r\n \t<li>Introduction to Nuclear Physics \u2013 by Keneth S Krane.<\/li>\r\n \t<li>Introductory Nuclear Physics \u2013 by Samuel S M Wong.<\/li>\r\n \t<li>Nuclear Physics \u2013 by R R Roy &amp; B P<span style=\"text-align: initial;font-size: 1em\"> Nigam.<\/span><\/li>\r\n \t<li>Handbook of Physics by Condon and Odishaw, TMH NewYork.<\/li>\r\n \t<li>Introduction to Nuclear Physics, 2nd Edition, W.N.Cottingham &amp; D.A. Greenwood.<\/li>\r\n \t<li>Concept<span style=\"text-align: initial;font-size: 1em\"> of Nuclear Physics by B L Cohen, McGraw Hill.<\/span><\/li>\r\n \t<li>Experimental techniques in Nuclear Physics by Dorin N. Poenaru &amp; Walter Greiner<\/li>\r\n \t<li>Exotic Nuclear Excitation by S.C. Pancholi<\/li>\r\n \t<li>Nuclear spectroscopy Part B, by Fay Ajzenberg- Selove<\/li>\r\n \t<li>Theory and Problems of modern<span style=\"text-align: initial;font-size: 1em\"> Physics (Schaum\u2019s <\/span>outline<span style=\"text-align: initial;font-size: 1em\"> Series)<\/span><\/li>\r\n \t<li>Basic Ideas &amp; Concepts in Nuclear Physics \u2013 by K Heyde<\/li>\r\n \t<li>The \u201cParticles of Modern Physics\u201d by J. D. Stranathan, Philadephia: Blakiston.<\/li>\r\n \t<li>Nuclear Physics by Irving Kaplan, Narosa Publishing House.<\/li>\r\n<\/ol>\r\n<strong><em>\u00a0 \u00a0Web Links<\/em><\/strong>\r\n<ol>\r\n \t<li style=\"text-align: justify\"><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 style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/0168900289907067\">http:\/\/www.sciencedirect.com\/science\/article\/pii\/0168900289907067<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/personal.ph.surrey.ac.uk\/~phs1pr\/lecture_notes\/nuc_expt_phr03.pdf\">http:\/\/personal.ph.surrey.ac.uk\/~phs1pr\/lecture_notes\/nuc_expt_phr03.pdf<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.wheldon.talktalk.net\/thesis\/thesis\/node34.html\">http:\/\/www.wheldon.talktalk.net\/thesis\/thesis\/node34.html<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.iaea.org\/inis\/collection\/NCLCollectionStore\/_Public\/29\/003\/29003562.pdf\">http:\/\/www.iaea.org\/inis\/collection\/NCLCollectionStore\/_Public\/29\/003\/29003562.pdf<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.annualreviews.org\/doi\/pdf\/10.1146\/annurev.ns.12.120162.000355\">http:\/\/www.annualreviews.org\/doi\/pdf\/10.1146\/annurev.ns.12.120162.000355<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/puhep1.princeton.edu\/~mcdonald\/e166\/pol%20papers\/fagg_rmp_31_711_59.pdf\">http:\/\/puhep1.princeton.edu\/~mcdonald\/e166\/pol%20papers\/fagg_rmp_31_711_59.pdf<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/lib.dr.iastate.edu\/cgi\/viewcontent.cgi?article=4892&amp;context=rtd\">http:\/\/lib.dr.iastate.edu\/cgi\/viewcontent.cgi?article=4892&amp;context=rtd<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/journals.aps.org\/pr\/abstract\/10.1103\/PhysRev.108.164\">http:\/\/journals.aps.org\/pr\/abstract\/10.1103\/PhysRev.108.164<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/scholarworks.wmich.edu\/cgi\/viewcontent.cgi?article=1277&amp;context=honors_theses\">http:\/\/scholarworks.wmich.edu\/cgi\/viewcontent.cgi?article=1277&amp;context=honors_theses<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/link.springer.com\/article\/10.1007%2FBF00173754#page-1\">http:\/\/link.springer.com\/article\/10.1007%2FBF00173754#page-1<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/arxiv.org\/ftp\/arxiv\/papers\/1308\/1308.0119.pdf\">https:\/\/arxiv.org\/ftp\/arxiv\/papers\/1308\/1308.0119.pdf<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/nuclear\/nspin.html\">http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/nuclear\/nspin.html<\/a><\/li>\r\n \t<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/link.springer.com\/article\/10.1007%2FBF01285045\">http:\/\/link.springer.com\/article\/10.1007%2FBF01285045<\/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<ul>\r\n \t<li style=\"text-align: justify\"><strong>\u00a0<\/strong><span style=\"text-align: justify;font-size: 1em\">The spin of nuclei in any state (ground\/excited) can be experimentally determined by measuring the angular distribution or the directional correlation (DCO) ratio while the parity can be determined by polarization measurement of de-excited gamma rays.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">For spin determination<span style=\"font-size: 1em\"> DCO measurement is preferred over angular distribution measurement due to <\/span>variety<span style=\"font-size: 1em\"> of advantages.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">For more sensitivity, DCO measurements are done with multi detector<span style=\"text-align: initial;font-size: 1em\"> arrays.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">For parity determination, polarization measurements are done with (linear\/circular\/elliptical) polarized gamma rays.<\/li>\r\n \t<li style=\"text-align: justify\">The linear polarization of gamma rays emitted from oriented states formed in nuclear reactions has a close relation to the angular distribution of these gamma rays. When gamma rays are linearly polarized, the angular distribution function of gamma rays depends not only on their outgoing direction with respect to the beam axis but also on their electric field direction with respect to the reaction plane, defined by an outgoing gamma ray and the beam axis.<\/li>\r\n \t<li style=\"text-align: justify\">The linear polarization of photons is quantum-mechanically defined as a normalized difference in the number of photons occupying two polarization states.<\/li>\r\n \t<li style=\"text-align: justify\">So, the linear polarization of gamma rays can be expressed in terms of the angular distribution functions when their electric field is in the reaction plane, and when it is perpendicular to the reaction plane,<\/li>\r\n \t<li style=\"text-align: justify\">The polarization has a maximum value in magnitudes at\u00a0 \u00a00 = 90'.<\/li>\r\n \t<li style=\"text-align: justify\">If we determine the polarization of gamma rays experimentally, the spin and the parity<span style=\"font-size: 1em\"> will be obtained by comparison with the calculated polarization <\/span>values.<\/li>\r\n \t<li style=\"text-align: justify\">The method to measure the linear polarization of gamma rays is based on Compton scattering.<\/li>\r\n \t<li style=\"text-align: justify\">In conventional<span style=\"text-align: initial;font-size: 1em\"> method of polarization measurements of gamma rays, one usually employs a detection geometry in which two absorbers surrounding a scatterer are placed perpendicularly to each other.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Also, one can conveniently measure the linear polarization by arranging the scatterer and absorbers in a way such that the first Compton-scattering plane is perpendicular to the reaction plane while the second Compton-scattering plane matches the reaction plane. For this geometry, the intensity of the Compton-scattered gamma rays counted by absorber 1 and absorber 2 is denoted by N|| and N ,<span style=\"text-align: initial;font-size: 1em\"> respectively.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Each of these intensity<span style=\"text-align: initial;font-size: 1em\"> is proportional to the differential cross section of Compton scattering and also to the angular distribution function.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Once the sensitivity as a function of the incident gamma-ray energy is known, the linear polarization of the gamma rays can be directly found by using the asymmetry measurement.<\/li>\r\n \t<li style=\"text-align: justify\">As the distance between a scatterer and an absorber is increased, the sensitivity increases because<span style=\"text-align: initial;font-size: 1em\"> the solid angle decreases; however, the coincidence efficiency gets lower. Thus, the overall quality of a Compton polarimeter depends not only on the sensitivity but also on the coincidence efficiency.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<strong><em>\u00a0 \u00a0 \u00a0Biography:<\/em><\/strong>\r\n<ol>\r\n \t<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Arthur_Compton\">https:\/\/en.wikipedia.org\/wiki\/Arthur_Compton<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1927\/compton-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1927\/compton-bio.html<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.thefamouspeople.com\/profiles\/arthur-compton-4646.php\">http:\/\/www.thefamouspeople.com\/profiles\/arthur-compton-4646.php<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.nasonline.org\/publications\/biographical-memoirs\/memoir-pdfs\/compton-arthur-h.pdf\">http:\/\/www.nasonline.org\/publications\/biographical-memoirs\/memoir-pdfs\/compton-arthur-h.pdf<\/a><\/li>\r\n \t<li><a href=\"http:\/\/www.chem.umn.edu\/groups\/taton\/chem8361\/Handouts\/9_7.pdf\">http:\/\/www.chem.umn.edu\/groups\/taton\/chem8361\/Handouts\/9_7.pdf<\/a><\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/VHx6Tq-mbZk\" 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 basic nuclear properties.<\/li>\n<li>The importance of nuclear properties.<\/li>\n<li>The experimental ways of determining nuclear properties.<\/li>\n<\/ul>\n<p><strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 1. Spin<\/strong><\/p>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-63 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23.png\" alt=\"\" width=\"887\" height=\"133\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23.png 887w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23-300x45.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23-768x115.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23-65x10.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23-225x34.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-23-350x52.png 350w\" sizes=\"auto, (max-width: 887px) 100vw, 887px\" \/><\/p>\n<\/div>\n<div>\n<p style=\"text-align: justify\">\u00a0 1.1. <strong>Directional Correlation Ratio (DCO- ratio)<\/strong> :The information about the DCO ratios is obtained in experiments with multi detector arrays in which the detectors should be placed at different angles with respect to the beam direction. The DCO ratio method is an important tool to infer the spin differences between states observed by the coincidence measurement of the gamma-decay between them.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">1.1.1.\u00a0\u00a0 <strong>Importance of DCO ratio : <\/strong>In comparison to the angular distribution, the DCO ratio is advantages in the sense that<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 weak transitions can be studied,<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 members of multiplets can be analysed and<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 no normalisation to the beam charge is necessary<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 By use of multidetector arrays the statistical accuracy of the DCO ratios can be increased by analysing many detector combinations .<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">1.1.2 <strong>Calculation of DCO ratio :<\/strong> For most applications the theory of DCO ratios can be simplified with respect to the general directional correlation theory by taking into account the experimental conditions (i) that unpolarized beams are used and (ii) that the detectors are insensitive to the polarization of the -y-rays. Therefore, detectors placed at forward and backward angles with respect to the beam direction can be treated in the same way. The angular correlation of -y-rays emitted from oriented states depends on the spins of the involved levels, the multipolarities and mixing ratios of the -transitions and the m-substate population distribution of the initial state. In the experiment a compound nucleus is produced via fusion evaporation reaction by bombarding a target nucleus with a projectile. The compound nucleus then start decaying by emitting -ray and come to the lower energy state. The -ray from the decaying nucleus are mostly of dipole or quadrupole nature or a mixture of both types. Suppose two detectors 1 and 2, placed at different angles as shown in figure 1, are used to determine the angular correlation of a cascade of two -rays. The detectors are making an angle \u03b81 and \u03b82 with the beam direction. The angle between the planes opened by each detector and the beam axis is.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-64 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24.png\" alt=\"\" width=\"889\" height=\"168\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24.png 889w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24-300x57.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24-768x145.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24-65x12.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24-225x43.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-24-350x66.png 350w\" sizes=\"auto, (max-width: 889px) 100vw, 889px\" \/><\/p>\n<\/div>\n<p><strong>\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-65 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25.png\" alt=\"\" width=\"803\" height=\"346\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25.png 803w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25-300x129.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25-768x331.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25-65x28.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25-225x97.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-25-350x151.png 350w\" sizes=\"auto, (max-width: 803px) 100vw, 803px\" \/><\/strong><\/p>\n<div>\n<p style=\"text-align: center\"><strong>Fig. 1: <\/strong>Geometry of the detector arrangement with the beam as orientation axis.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-66\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-26.png\" alt=\"\" width=\"790\" height=\"552\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-68 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-27.png\" alt=\"\" width=\"558\" height=\"333\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong style=\"text-align: initial;font-size: 1em\">Fig. 2: <\/strong><span style=\"text-align: initial;font-size: 1em\">The picture of Indian National Gamma Array (INGA) at TIFR, Mumbai.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-69 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-28.png\" alt=\"\" width=\"583\" height=\"382\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Fig. 3: <\/strong>DCO Ratio of the transitions belonging to the band gated by 958 keV transition.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The value of RDCO is approximately unity for quadrupole transition and non stretched dipole, the value between 0.4 and 0.6 for stretched dipole and the value between 0.6 and 0.8 implies a mixed transition.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>1.1.3 Limitations of DCO ratio method : <\/strong>Though the DCO ratio method is advantageous and therefore preferred over angular distribution measurements method, it has its limitation too. The serious disadvantage is that with this method a spin change of I = \u00b1 1 cannot be distinguished.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>2. Parity<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The parity of a nuclear state can efficiently be determined by measuring the electric and magnetic nature of de-exciting -rays (Linear polarization). The sign of the measured linear polarization\u00a0<span style=\"text-align: initial;font-size: 1em\">distinguishes electric and magnetic types of gamma-ray transitions. Electric transitions have preferential scattering along the perpendicular direction, while magnetic transitions have scattering along parallel direction. Depending on the energy of -ray, Compton scattering, e&#8211; e+ pair production and photoelectric effect can be used for measuring the degree of polarization. The linear polarization along with the angular distribution or DCO ratios measurements can uniquely determine the spins &amp; parities of nuclear states<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2.1 Polarization measurement in nuclei : <\/strong><span style=\"text-align: initial;font-size: 1em\">A conventional Compton polarimeter, used to determine the <\/span>parities<span style=\"text-align: initial;font-size: 1em\"> of different levels in 155Gd is shown in figure 4. It has one scatterer and two absorbers\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">with 25 segments on the front face of a germanium crystal, each of which acts an individual gamma-ray detector. In this polarimeter, there are three planes and four relevant angles to define the linear polarization of the gamma rays.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-70 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-29.png\" alt=\"\" width=\"457\" height=\"258\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-29.png 457w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-29-300x169.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-29-65x37.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-29-225x127.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-29-350x198.png 350w\" sizes=\"auto, (max-width: 457px) 100vw, 457px\" \/><\/p>\n<p>Fig. 4: A picture of a conventional Compton polarimeter consisting of one scatterer and two absorbers.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The linear polarization of gamma rays emitted from oriented states formed in nuclear reactions and the angular distribution of the gamma rays are related to each other. For a linear polarized gamma rays, the angular distribution function depends not on their outgoing direction, \u03b8 with respect to the beam axis and their electric field direction, \u03b5 with respect to the reaction plane. The linear polarization of -rays can be expressed in terms of the angular distribution functions when their electric field is in the reaction plane, W(\u03b8, \u03b5 = 00), and when it is perpendicular to the reaction plane, W(\u03b8, \u03b5 = 90&#8242;). i.e;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-71 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-30.png\" alt=\"\" width=\"700\" height=\"125\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-30.png 700w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-30-300x54.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-30-65x12.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-30-225x40.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-30-350x63.png 350w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/p>\n<\/div>\n<p style=\"text-align: justify\"><strong>\u00a0<\/strong><strong style=\"text-align: initial;font-size: 1em\">2.2 Calculating polarization coefficients theoretically : <\/strong><span style=\"text-align: initial;font-size: 1em\">The polarization coefficients for pure (electric\/magnetic) dipole and the (electric) quadrupole transitions in terms of angular distribution parameters a2 and a4 can be derived as:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-72 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-31.png\" alt=\"\" width=\"726\" height=\"174\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-31.png 726w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-31-300x72.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-31-65x16.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-31-225x54.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-31-350x84.png 350w\" sizes=\"auto, (max-width: 726px) 100vw, 726px\" \/><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: justify;font-size: 1em\">From the above equations, the maximum value of the polarization in magnitudes at = 90&#8242;. Theoretically calculated values of polarization coefficients for pure (electric\/ magnetic) dipole and the (electric) quadrupole transitions are listed in table 1.<\/span><\/p>\n<\/div>\n<div>\n<p><strong>Table 1: <\/strong>Theoretically calculated values of polarization coefficients for pure (electric\/ magnetic) dipole and the (electric) quadrupole transitions.<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-73 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-32.png\" alt=\"\" width=\"778\" height=\"548\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-74 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-33.png\" alt=\"\" width=\"743\" height=\"744\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-33-150x150.png 150w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-33-65x64.png 65w\" sizes=\"auto, (max-width: 743px) 100vw, 743px\" \/><\/p>\n<ol start=\"3\">\n<li style=\"text-align: justify\"><strong>Summary : <\/strong>The spin and parity of important nuclear properties. Knowing the spin and parity of a nuclear eigen state can reveal the underlying single particle configurations involved in the formation of that state. Both, the spin and parity of a nuclear state can be determined experimentally. The spin can be obtained by determining the multipole order and the dipole-quadrupole mixing ratio ( ) of the outgoing gamma radiation. To get the two parameters, measuring DCO ratio is better than the angular distribution, accurate measurements need multi-detector array. The parity of a nuclear state can be obtained by measuring the polarization of outgoing gamma rays. It can be concluded that the investigation of DCO ratios allows the determination of spins and dipole-quadrupole mixing ratios.<\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Basic nuclear properties-5<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/VHx6Tq-mbZk\" 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<div>\n<p><strong><em>\u00a0 \u00a0 \u00a0References:<\/em><\/strong><\/p>\n<ol>\n<li>Introduction to Nuclear Physics \u2013 by Keneth S Krane.<\/li>\n<li>Introductory Nuclear Physics \u2013 by Samuel S M Wong.<\/li>\n<li>Nuclear Physics \u2013 by R R Roy &amp; B P<span style=\"text-align: initial;font-size: 1em\"> Nigam.<\/span><\/li>\n<li>Handbook of Physics by Condon and Odishaw, TMH NewYork.<\/li>\n<li>Introduction to Nuclear Physics, 2nd Edition, W.N.Cottingham &amp; D.A. Greenwood.<\/li>\n<li>Concept<span style=\"text-align: initial;font-size: 1em\"> of Nuclear Physics by B L Cohen, McGraw Hill.<\/span><\/li>\n<li>Experimental techniques in Nuclear Physics by Dorin N. Poenaru &amp; Walter Greiner<\/li>\n<li>Exotic Nuclear Excitation by S.C. Pancholi<\/li>\n<li>Nuclear spectroscopy Part B, by Fay Ajzenberg- Selove<\/li>\n<li>Theory and Problems of modern<span style=\"text-align: initial;font-size: 1em\"> Physics (Schaum\u2019s <\/span>outline<span style=\"text-align: initial;font-size: 1em\"> Series)<\/span><\/li>\n<li>Basic Ideas &amp; Concepts in Nuclear Physics \u2013 by K Heyde<\/li>\n<li>The \u201cParticles of Modern Physics\u201d by J. D. Stranathan, Philadephia: Blakiston.<\/li>\n<li>Nuclear Physics by Irving Kaplan, Narosa Publishing House.<\/li>\n<\/ol>\n<p><strong><em>\u00a0 \u00a0Web Links<\/em><\/strong><\/p>\n<ol>\n<li style=\"text-align: justify\"><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 style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/0168900289907067\">http:\/\/www.sciencedirect.com\/science\/article\/pii\/0168900289907067<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/personal.ph.surrey.ac.uk\/~phs1pr\/lecture_notes\/nuc_expt_phr03.pdf\">http:\/\/personal.ph.surrey.ac.uk\/~phs1pr\/lecture_notes\/nuc_expt_phr03.pdf<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.wheldon.talktalk.net\/thesis\/thesis\/node34.html\">http:\/\/www.wheldon.talktalk.net\/thesis\/thesis\/node34.html<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.iaea.org\/inis\/collection\/NCLCollectionStore\/_Public\/29\/003\/29003562.pdf\">http:\/\/www.iaea.org\/inis\/collection\/NCLCollectionStore\/_Public\/29\/003\/29003562.pdf<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/www.annualreviews.org\/doi\/pdf\/10.1146\/annurev.ns.12.120162.000355\">http:\/\/www.annualreviews.org\/doi\/pdf\/10.1146\/annurev.ns.12.120162.000355<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/puhep1.princeton.edu\/~mcdonald\/e166\/pol%20papers\/fagg_rmp_31_711_59.pdf\">http:\/\/puhep1.princeton.edu\/~mcdonald\/e166\/pol%20papers\/fagg_rmp_31_711_59.pdf<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/lib.dr.iastate.edu\/cgi\/viewcontent.cgi?article=4892&amp;context=rtd\">http:\/\/lib.dr.iastate.edu\/cgi\/viewcontent.cgi?article=4892&amp;context=rtd<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/journals.aps.org\/pr\/abstract\/10.1103\/PhysRev.108.164\">http:\/\/journals.aps.org\/pr\/abstract\/10.1103\/PhysRev.108.164<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/scholarworks.wmich.edu\/cgi\/viewcontent.cgi?article=1277&amp;context=honors_theses\">http:\/\/scholarworks.wmich.edu\/cgi\/viewcontent.cgi?article=1277&amp;context=honors_theses<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/link.springer.com\/article\/10.1007%2FBF00173754#page-1\">http:\/\/link.springer.com\/article\/10.1007%2FBF00173754#page-1<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"https:\/\/arxiv.org\/ftp\/arxiv\/papers\/1308\/1308.0119.pdf\">https:\/\/arxiv.org\/ftp\/arxiv\/papers\/1308\/1308.0119.pdf<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/nuclear\/nspin.html\">http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/nuclear\/nspin.html<\/a><\/li>\n<li style=\"text-align: justify\"><a style=\"text-align: initial;font-size: 1em\" href=\"http:\/\/link.springer.com\/article\/10.1007%2FBF01285045\">http:\/\/link.springer.com\/article\/10.1007%2FBF01285045<\/a><\/li>\n<\/ol>\n<\/div>\n<div>\n<p><strong>\u00a0 \u00a0\u00a0<\/strong><strong>Did you know ?<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify\"><strong>\u00a0<\/strong><span style=\"text-align: justify;font-size: 1em\">The spin of nuclei in any state (ground\/excited) can be experimentally determined by measuring the angular distribution or the directional correlation (DCO) ratio while the parity can be determined by polarization measurement of de-excited gamma rays.<\/span><\/li>\n<li style=\"text-align: justify\">For spin determination<span style=\"font-size: 1em\"> DCO measurement is preferred over angular distribution measurement due to <\/span>variety<span style=\"font-size: 1em\"> of advantages.<\/span><\/li>\n<li style=\"text-align: justify\">For more sensitivity, DCO measurements are done with multi detector<span style=\"text-align: initial;font-size: 1em\"> arrays.<\/span><\/li>\n<li style=\"text-align: justify\">For parity determination, polarization measurements are done with (linear\/circular\/elliptical) polarized gamma rays.<\/li>\n<li style=\"text-align: justify\">The linear polarization of gamma rays emitted from oriented states formed in nuclear reactions has a close relation to the angular distribution of these gamma rays. When gamma rays are linearly polarized, the angular distribution function of gamma rays depends not only on their outgoing direction with respect to the beam axis but also on their electric field direction with respect to the reaction plane, defined by an outgoing gamma ray and the beam axis.<\/li>\n<li style=\"text-align: justify\">The linear polarization of photons is quantum-mechanically defined as a normalized difference in the number of photons occupying two polarization states.<\/li>\n<li style=\"text-align: justify\">So, the linear polarization of gamma rays can be expressed in terms of the angular distribution functions when their electric field is in the reaction plane, and when it is perpendicular to the reaction plane,<\/li>\n<li style=\"text-align: justify\">The polarization has a maximum value in magnitudes at\u00a0 \u00a00 = 90&#8242;.<\/li>\n<li style=\"text-align: justify\">If we determine the polarization of gamma rays experimentally, the spin and the parity<span style=\"font-size: 1em\"> will be obtained by comparison with the calculated polarization <\/span>values.<\/li>\n<li style=\"text-align: justify\">The method to measure the linear polarization of gamma rays is based on Compton scattering.<\/li>\n<li style=\"text-align: justify\">In conventional<span style=\"text-align: initial;font-size: 1em\"> method of polarization measurements of gamma rays, one usually employs a detection geometry in which two absorbers surrounding a scatterer are placed perpendicularly to each other.<\/span><\/li>\n<li style=\"text-align: justify\">Also, one can conveniently measure the linear polarization by arranging the scatterer and absorbers in a way such that the first Compton-scattering plane is perpendicular to the reaction plane while the second Compton-scattering plane matches the reaction plane. For this geometry, the intensity of the Compton-scattered gamma rays counted by absorber 1 and absorber 2 is denoted by N|| and N ,<span style=\"text-align: initial;font-size: 1em\"> respectively.<\/span><\/li>\n<li style=\"text-align: justify\">Each of these intensity<span style=\"text-align: initial;font-size: 1em\"> is proportional to the differential cross section of Compton scattering and also to the angular distribution function.<\/span><\/li>\n<li style=\"text-align: justify\">Once the sensitivity as a function of the incident gamma-ray energy is known, the linear polarization of the gamma rays can be directly found by using the asymmetry measurement.<\/li>\n<li style=\"text-align: justify\">As the distance between a scatterer and an absorber is increased, the sensitivity increases because<span style=\"text-align: initial;font-size: 1em\"> the solid angle decreases; however, the coincidence efficiency gets lower. Thus, the overall quality of a Compton polarimeter depends not only on the sensitivity but also on the coincidence efficiency.<\/span><\/li>\n<\/ul>\n<\/div>\n<p><strong><em>\u00a0 \u00a0 \u00a0Biography:<\/em><\/strong><\/p>\n<ol>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Arthur_Compton\">https:\/\/en.wikipedia.org\/wiki\/Arthur_Compton<\/a><\/li>\n<li><a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1927\/compton-bio.html\">http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1927\/compton-bio.html<\/a><\/li>\n<li><a href=\"http:\/\/www.thefamouspeople.com\/profiles\/arthur-compton-4646.php\">http:\/\/www.thefamouspeople.com\/profiles\/arthur-compton-4646.php<\/a><\/li>\n<li><a href=\"http:\/\/www.nasonline.org\/publications\/biographical-memoirs\/memoir-pdfs\/compton-arthur-h.pdf\">http:\/\/www.nasonline.org\/publications\/biographical-memoirs\/memoir-pdfs\/compton-arthur-h.pdf<\/a><\/li>\n<li><a href=\"http:\/\/www.chem.umn.edu\/groups\/taton\/chem8361\/Handouts\/9_7.pdf\">http:\/\/www.chem.umn.edu\/groups\/taton\/chem8361\/Handouts\/9_7.pdf<\/a><\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":3,"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-59","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\/59","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":7,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters\/59\/revisions"}],"predecessor-version":[{"id":337,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters\/59\/revisions\/337"}],"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\/59\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/media?parent=59"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapter-type?post=59"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/contributor?post=59"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/license?post=59"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}