{"id":38,"date":"2018-11-02T09:03:29","date_gmt":"2018-11-02T09:03:29","guid":{"rendered":"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=38"},"modified":"2022-01-07T05:30:46","modified_gmt":"2022-01-07T05:30:46","slug":"basic-nuclear-properties-4","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/chapter\/basic-nuclear-properties-4\/","title":{"rendered":"Basic nuclear properties-4"},"content":{"raw":"<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 1.3 Mirror nuclei method:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">\u201cMirror nuclei\u201d are pairs of nuclei in which the proton number in one equals the neutron number in the other and vice versa. Some examples of mirror nuclei are listed in table 1. The nuclei in these pairs differ from each other only in that a proton in one is exchanged for the neutron in the other. If we accept the principle of charge symmetry according to which the nuclear force between a pair of protons is the same as the force between a pair of neutrons in the same state, than there should be no difference in the nuclear binding forces of a pair of mirror nuclei but experimentally it was observed that the total binding energy of the two nuclei will not be the same, however, because of the difference in the coulomb self-energy.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n<p style=\"text-align: center;\">Table 1<\/p>\r\n<img class=\"wp-image-43 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-10.png\" alt=\"\" width=\"713\" height=\"235\" \/>\r\n\r\nFor a pair of mirror nuclei of radius R, charges Ze and (Z+1)e, the coulomb energy difference is given by\r\n\r\n<\/div>\r\n<img class=\"wp-image-44 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-11.png\" alt=\"\" width=\"744\" height=\"312\" \/>\r\n<div><\/div>\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial; font-size: 1em;\">1.4 Mesonic X-ray method:<\/strong>\r\n<div>\r\n\r\n<img class=\"wp-image-45 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-12.png\" alt=\"\" width=\"766\" height=\"476\" \/>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"size-full wp-image-46 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-13.png\" alt=\"\" width=\"261\" height=\"256\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">Fig 1: A X-ray spectrum of Ti nuclei. Observed peak was found at energy 0.955 MeV.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><span style=\"font-size: 1em; text-align: initial;\">Table 2<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"wp-image-47 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-14.png\" alt=\"\" width=\"575\" height=\"236\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>2. Measuring nuclear masss:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\">The mass of nuclei is an important nuclear property that needs to be measured as precisely as possible. Just to show as how important are nuclear mass measurements, we can consider the example of nuclei produced by the cosmic radiations in the upper atmosphere. When cosmic radiation interacts with the atmosphere and the surface layers of Earth, minute quantities of radioactive nuclei (such as carbon, aluminium and chlorine) are produced. These isotopes decay sufficiently slowly to be useful in dating human artefacts or natural features in the environment. So to know which nuclei and of what mass have been produced in these nuclei is important to know the quality of soil.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong>Methods of measurements : <\/strong>The nuclear masses can be measured by variety of ways. However the principle methods used to measure mass of nuclei are the followings :<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong>2.1 Via Q- value determination in nuclear reaction or decay <\/strong>: In this method, first the mass difference of nuclei are found by measuring the Q-value (total energy released) of the reaction or decay happening. For example in the 2-body reaction a(b,c)d, the mass excess ( ) are related by<\/p>\r\n<p style=\"text-align: justify;\"><img class=\"wp-image-48 alignleft\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-15.png\" alt=\"\" width=\"799\" height=\"107\" \/><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nmeasure the mass of the remaining reaction partner.\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">In addition to the measurements in nuclear reactions, the mass of nuclei can also be found by measuring the Q-value of a nuclear decay. In <\/span>principle<span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\"> the masses for all bound nuclei off the stability line can be determined from the measurement of the Q- value associated with the -decay. This approach has, consequently, been employed across a wide range of nuclei in association with most production methods.<\/span><\/p>\r\n&nbsp;\r\n\r\n<span style=\"text-align: initial; font-size: 1em;\">In the case of nuclei on the neutron-rich side of stability, decay is accompanied by the emission of an electron, i.e.<\/span>\r\n\r\n<img class=\"alignnone wp-image-50 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-16.png\" alt=\"\" width=\"762\" height=\"34\" \/>\r\n\r\n<span style=\"text-align: initial; font-size: 1em;\">and the mass difference is simply,<\/span>\r\n<div>\r\n\r\n<img class=\"wp-image-51 size-full alignleft\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-17.png\" alt=\"\" width=\"763\" height=\"142\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\">Usually the mass of the daughter (d) is known and the mass of the parent (a) may be deduced. Decay may occur to either the ground or excited states of the daughter and in the latter case, the mass differences must be adjusted by the excitation energy of the state fed by the measured transition. Far from stability, however, decay schemes are often poorly known and it is necessary to measure the -particles in coincidence with gamma rays in order to establish the decay scheme. Then, the Q- value for the decay is derived from the feedings to a number of excited states as well as to the ground state.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong>2.2 Via Decay counting method :<\/strong>The method is the earliest (and also the conventional) method of measuring mass and the abundance of radioactive nuclei by observing the decay produced by them. Decay counting methods are used for fast-decaying radioactive isotopes. By measuring the number of alpha or beta decays in a given period of time and comparing with known decay rates, the abundance of a radioactive isotope may be calculated. This method is extensively used to determine the activity or concentration of radioactive isotopes. Methods include gas proportional counting and liquid scintillation counting. The basic principle of measuring mass (or nuclear abundances) is shown in the figure given below.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"wp-image-52 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-18.png\" alt=\"\" width=\"440\" height=\"317\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">Fig 2: Principle of measuring mass via decay counting method.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Nowadays, the decay counting method is not a very popular method of finding nuclear abundances as it is <\/span>time consuming<span style=\"text-align: initial; font-size: 1em;\"> and requires strong radioactive sources to get the desired accuracy. The more sophisticated, accurate and less <\/span>time consuming<span style=\"text-align: initial; font-size: 1em;\"> methods like accelerator mass spectrometry are commonly used.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">2.3 Via Direct measurement methods (e.g. Accelerator mass spectrometry (AMS)) :<\/strong><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">All direct mass measurement techniques work on the same basic principle, namely that the magnetic rigidity (Bp) is related to the <\/span>time-of- flight<span style=\"text-align: initial; font-size: 1em;\"> (TOF) through the system in question, or the cyclotron frequency. The most popular direct technique of mass measurement is Accelerator mass spectrometry (AMS).<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><img class=\"alignnone wp-image-54 \" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-19.png\" alt=\"\" width=\"794\" height=\"268\" \/><\/p>\r\n\r\n<\/div>\r\n<div>\r\n<p style=\"text-align: justify;\"><strong>\u00a0 \u00a0 2.3.1.1 Principle of working : <\/strong>The AMS work on the principle of counting of individual nuclei. The sample is put into a negative ion source. The negative ions are injected into the positive terminal of an accelerator where all molecular ions are broken up and positive ions are formed. The positive ions are again accelerated and mass\/energy analyzed to separate the abundant and rare isotopes. In general the working of AMS involves the following steps :<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">(a)\u00a0 Negatively charged ions from the material to be analysed are injected into a nuclear particle accelerator.<\/p>\r\n<p style=\"text-align: justify;\">(b) The negative ions are then accelerated towards the positive potential. At the terminal they pass through either a very thin carbon film or a tube filled with gas at low pressure (the stripper), depending on the particular accelerator. Collisions with carbon or gas atoms in the stripper remove several electrons from the carbon ions, changing their polarity from negative to positive.<\/p>\r\n<p style=\"text-align: justify;\">(c) The positive ions are accelerated through the second stage of the accelerator, reaching kinetic energies of the order of 10 to 30 million electron volts. This has the effect of eliminating the 14N ions that are extremely common in the Earth\u2019s atmosphere.<\/p>\r\n<p style=\"text-align: justify;\">(d) The ions are then subjected to perpendicular (to their direction of motion) magnetic field inside a magnetic spectrometer. The ions are then dispersed as per their mass \u2013to-charge ratio (m\/q).<\/p>\r\n<p style=\"text-align: justify;\">(e) The separated ions are then collected\/detected in a suitable particle detector. The detector may be a solid-state detector or a device based on the gridded ionisation chamber. The latter type of detector can measure both the total energy of the incoming ion, and also the rate at which it slows down as it passes\u00a0<span style=\"text-align: initial; font-size: 1em;\">through the gas-filled detector. These two pieces of information are sufficient to completely identify the ions.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"wp-image-55 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-20.png\" alt=\"\" width=\"567\" height=\"265\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">Fig 3: Principle of measuring mass via decay counting method.<\/p>\r\n&nbsp;\r\n\r\n<strong>2.3.1.2 Essential components : <\/strong>A typical AMS system essentially includes the following:\r\n\r\n&nbsp;\r\n\r\n<img class=\"wp-image-56 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-21.png\" alt=\"\" width=\"689\" height=\"225\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">Fig 4: Schematic diagram showing essential components of a mass spectrometer.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong>Ion source : <\/strong>The sample material containing the rare isotopes to be counted is placed in the ion source. The neutral atoms are converted into the negatively charged ions. This is required because all mass spectrometers use E.M. fields to manipulate atoms and the atoms must be charged (and hence be ions) to be manipulated. The AMS systems based on tandem electrostatic accelerators employ ion sources which utilize a beam of Cs+ ions to sputter material from the sample. The ion source also provides some degree of focusing, collimation &amp; acceleration to ions. Most mass spectrometers use positive ions, since they are in general more easily created, but sometimes using negative ions is required.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">Mass Analyzer : <\/strong><span style=\"text-align: initial; font-size: 1em;\">is a filter that separates ions by mass (or more specifically by momentum or energy) in space or in time by using a combination of electric and magnetic fields (RF fields). It also <\/span>provide<span style=\"text-align: initial; font-size: 1em;\"> some degree of focusing to compensate for any optical spread of the ion beam leaving the source. <\/span>Usually<span style=\"text-align: initial; font-size: 1em;\"> the choice of mass separator &amp; ion source is guided by the following parameters : (a) sample character, i.e. is the sample a gas, liquid, solid&amp; in what state of purity? (b) The abundance of <\/span>isotope<span style=\"text-align: initial; font-size: 1em;\"> in the material, i.e. how abundant is the material? Is it common or trace? (c) isotopic abundance, i.e. are the isotopes of interest all of <\/span>similar<span style=\"text-align: initial; font-size: 1em;\"> abundance, or are they drastically different? (d) <\/span>range<span style=\"text-align: initial; font-size: 1em;\"> of variation, i.e. do the isotope ratios vary a lot or a little? ( e) Are there any interferences, i.e. are there isotopes of another element or compounds\/isotopes of similar m\/e (mass to charge ratio) that must be eliminated or separated? (f) our requirement, i.e. whether absolute or relative ratios are needed.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">Detector: <\/strong><span style=\"text-align: initial; font-size: 1em;\">The <\/span>iidentification<span style=\"text-align: initial; font-size: 1em;\"> and counting of the individual rare isotopes <\/span>is<span style=\"text-align: initial; font-size: 1em;\"> done with nuclear detection techniques to measure ions leaving mass analyzer. The detection method mostly depends on the ion beam intensity which <\/span>range<span style=\"text-align: initial; font-size: 1em;\"> from a few ions per second to a fraction of a nano-ampere (109-1010 ions per second).<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">Computer controlled data acquisition system : <\/strong><span style=\"text-align: initial; font-size: 1em;\">In order to allow for an unattended operation of the identification process and to provide control of the AMS system parameters, a computer controlled data acquisition system is needed and the live images of the ions collected <\/span>is<span style=\"text-align: initial; font-size: 1em;\"> obtained.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"alignnone wp-image-57 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22.png\" alt=\"\" width=\"806\" height=\"491\" \/>\r\n\r\n<span style=\"text-align: initial; font-size: 1em;\">problems or, in some cases, itself influence the process being studied. AMS allows very low levels of tracer to be used, completely avoiding these problems.<\/span>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong style=\"text-align: justify; font-size: 1em;\">2.3.1.4 Limitations of AMS technique : <\/strong><span style=\"text-align: justify; font-size: 1em;\">The serious limitation of AMS is that it tends to be more expensive than decay counting. <\/span>Technique<span style=\"text-align: justify; font-size: 1em;\"> essentially uses an accelerator and purchasing and maintaining a particle accelerator and its associated components <\/span>is<span style=\"text-align: justify; font-size: 1em;\"> expensive.<\/span><\/p>\r\n&nbsp;\r\n\r\n<strong style=\"font-size: 1em;\">3. Summary:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">The knowledge of basic nuclear properties of nuclei and the ways of measuring them accurately is very important. The charge and mass are fundamental to any nucleus and therefore their accurate determination is essential. The nuclear charge can be measured in a variety of ways with each method have its own advantages and disadvantages. The method of measuring the charge distribution in nuclei with electron scattering method is very useful and give direct access to the nuclear environment. It gives a fairly accurate value of the charge distribution and is therefore considered as the best method so far. To measure the mass of nuclei, though a number of methods are available but owing to its accuracy, less <\/span>time consuming<span style=\"text-align: initial; font-size: 1em;\"> nature and other unique advantages, the accelerator mass spectrometer technique is more useful.<\/span><\/p>\r\n&nbsp;\r\n\r\n<\/div>","rendered":"<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 1.3 Mirror nuclei method:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">\u201cMirror nuclei\u201d are pairs of nuclei in which the proton number in one equals the neutron number in the other and vice versa. Some examples of mirror nuclei are listed in table 1. The nuclei in these pairs differ from each other only in that a proton in one is exchanged for the neutron in the other. If we accept the principle of charge symmetry according to which the nuclear force between a pair of protons is the same as the force between a pair of neutrons in the same state, than there should be no difference in the nuclear binding forces of a pair of mirror nuclei but experimentally it was observed that the total binding energy of the two nuclei will not be the same, however, because of the difference in the coulomb self-energy.<\/span><\/p>\n<\/div>\n<div>\n<p style=\"text-align: center;\">Table 1<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-43 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-10.png\" alt=\"\" width=\"713\" height=\"235\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-10.png 713w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-10-300x99.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-10-65x21.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-10-225x74.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-10-350x115.png 350w\" sizes=\"auto, (max-width: 713px) 100vw, 713px\" \/><\/p>\n<p>For a pair of mirror nuclei of radius R, charges Ze and (Z+1)e, the coulomb energy difference is given by<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-44 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-11.png\" alt=\"\" width=\"744\" height=\"312\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-11.png 744w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-11-300x126.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-11-65x27.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-11-225x94.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-11-350x147.png 350w\" sizes=\"auto, (max-width: 744px) 100vw, 744px\" \/><\/p>\n<div><\/div>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial; font-size: 1em;\">1.4 Mesonic X-ray method:<\/strong><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-45 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-12.png\" alt=\"\" width=\"766\" height=\"476\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-12.png 766w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-12-300x186.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-12-65x40.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-12-225x140.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-12-350x217.png 350w\" sizes=\"auto, (max-width: 766px) 100vw, 766px\" \/><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-46 aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-13.png\" alt=\"\" width=\"261\" height=\"256\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-13.png 261w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-13-65x64.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-13-225x221.png 225w\" sizes=\"auto, (max-width: 261px) 100vw, 261px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">Fig 1: A X-ray spectrum of Ti nuclei. Observed peak was found at energy 0.955 MeV.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 1em; text-align: initial;\">Table 2<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-47 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-14.png\" alt=\"\" width=\"575\" height=\"236\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-14.png 575w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-14-300x123.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-14-65x27.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-14-225x92.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-14-350x144.png 350w\" sizes=\"auto, (max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>2. Measuring nuclear masss:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">The mass of nuclei is an important nuclear property that needs to be measured as precisely as possible. Just to show as how important are nuclear mass measurements, we can consider the example of nuclei produced by the cosmic radiations in the upper atmosphere. When cosmic radiation interacts with the atmosphere and the surface layers of Earth, minute quantities of radioactive nuclei (such as carbon, aluminium and chlorine) are produced. These isotopes decay sufficiently slowly to be useful in dating human artefacts or natural features in the environment. So to know which nuclei and of what mass have been produced in these nuclei is important to know the quality of soil.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Methods of measurements : <\/strong>The nuclear masses can be measured by variety of ways. However the principle methods used to measure mass of nuclei are the followings :<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>2.1 Via Q- value determination in nuclear reaction or decay <\/strong>: In this method, first the mass difference of nuclei are found by measuring the Q-value (total energy released) of the reaction or decay happening. For example in the 2-body reaction a(b,c)d, the mass excess ( ) are related by<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-48 alignleft\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-15.png\" alt=\"\" width=\"799\" height=\"107\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>measure the mass of the remaining reaction partner.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">In addition to the measurements in nuclear reactions, the mass of nuclei can also be found by measuring the Q-value of a nuclear decay. In <\/span>principle<span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\"> the masses for all bound nuclei off the stability line can be determined from the measurement of the Q- value associated with the -decay. This approach has, consequently, been employed across a wide range of nuclei in association with most production methods.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-align: initial; font-size: 1em;\">In the case of nuclei on the neutron-rich side of stability, decay is accompanied by the emission of an electron, i.e.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-50 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-16.png\" alt=\"\" width=\"762\" height=\"34\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-16.png 762w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-16-300x13.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-16-65x3.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-16-225x10.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-16-350x16.png 350w\" sizes=\"auto, (max-width: 762px) 100vw, 762px\" \/><\/p>\n<p><span style=\"text-align: initial; font-size: 1em;\">and the mass difference is simply,<\/span><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-51 size-full alignleft\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-17.png\" alt=\"\" width=\"763\" height=\"142\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-17.png 763w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-17-300x56.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-17-65x12.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-17-225x42.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-17-350x65.png 350w\" sizes=\"auto, (max-width: 763px) 100vw, 763px\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Usually the mass of the daughter (d) is known and the mass of the parent (a) may be deduced. Decay may occur to either the ground or excited states of the daughter and in the latter case, the mass differences must be adjusted by the excitation energy of the state fed by the measured transition. Far from stability, however, decay schemes are often poorly known and it is necessary to measure the -particles in coincidence with gamma rays in order to establish the decay scheme. Then, the Q- value for the decay is derived from the feedings to a number of excited states as well as to the ground state.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>2.2 Via Decay counting method :<\/strong>The method is the earliest (and also the conventional) method of measuring mass and the abundance of radioactive nuclei by observing the decay produced by them. Decay counting methods are used for fast-decaying radioactive isotopes. By measuring the number of alpha or beta decays in a given period of time and comparing with known decay rates, the abundance of a radioactive isotope may be calculated. This method is extensively used to determine the activity or concentration of radioactive isotopes. Methods include gas proportional counting and liquid scintillation counting. The basic principle of measuring mass (or nuclear abundances) is shown in the figure given below.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-52 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-18.png\" alt=\"\" width=\"440\" height=\"317\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-18.png 440w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-18-300x216.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-18-65x47.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-18-225x162.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-18-350x252.png 350w\" sizes=\"auto, (max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">Fig 2: Principle of measuring mass via decay counting method.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Nowadays, the decay counting method is not a very popular method of finding nuclear abundances as it is <\/span>time consuming<span style=\"text-align: initial; font-size: 1em;\"> and requires strong radioactive sources to get the desired accuracy. The more sophisticated, accurate and less <\/span>time consuming<span style=\"text-align: initial; font-size: 1em;\"> methods like accelerator mass spectrometry are commonly used.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">2.3 Via Direct measurement methods (e.g. Accelerator mass spectrometry (AMS)) :<\/strong><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">All direct mass measurement techniques work on the same basic principle, namely that the magnetic rigidity (Bp) is related to the <\/span>time-of- flight<span style=\"text-align: initial; font-size: 1em;\"> (TOF) through the system in question, or the cyclotron frequency. The most popular direct technique of mass measurement is Accelerator mass spectrometry (AMS).<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-54\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-19.png\" alt=\"\" width=\"794\" height=\"268\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-19-300x102.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-19-65x22.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-19-225x77.png 225w\" sizes=\"auto, (max-width: 794px) 100vw, 794px\" \/><\/p>\n<\/div>\n<div>\n<p style=\"text-align: justify;\"><strong>\u00a0 \u00a0 2.3.1.1 Principle of working : <\/strong>The AMS work on the principle of counting of individual nuclei. The sample is put into a negative ion source. The negative ions are injected into the positive terminal of an accelerator where all molecular ions are broken up and positive ions are formed. The positive ions are again accelerated and mass\/energy analyzed to separate the abundant and rare isotopes. In general the working of AMS involves the following steps :<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">(a)\u00a0 Negatively charged ions from the material to be analysed are injected into a nuclear particle accelerator.<\/p>\n<p style=\"text-align: justify;\">(b) The negative ions are then accelerated towards the positive potential. At the terminal they pass through either a very thin carbon film or a tube filled with gas at low pressure (the stripper), depending on the particular accelerator. Collisions with carbon or gas atoms in the stripper remove several electrons from the carbon ions, changing their polarity from negative to positive.<\/p>\n<p style=\"text-align: justify;\">(c) The positive ions are accelerated through the second stage of the accelerator, reaching kinetic energies of the order of 10 to 30 million electron volts. This has the effect of eliminating the 14N ions that are extremely common in the Earth\u2019s atmosphere.<\/p>\n<p style=\"text-align: justify;\">(d) The ions are then subjected to perpendicular (to their direction of motion) magnetic field inside a magnetic spectrometer. The ions are then dispersed as per their mass \u2013to-charge ratio (m\/q).<\/p>\n<p style=\"text-align: justify;\">(e) The separated ions are then collected\/detected in a suitable particle detector. The detector may be a solid-state detector or a device based on the gridded ionisation chamber. The latter type of detector can measure both the total energy of the incoming ion, and also the rate at which it slows down as it passes\u00a0<span style=\"text-align: initial; font-size: 1em;\">through the gas-filled detector. These two pieces of information are sufficient to completely identify the ions.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-55 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-20.png\" alt=\"\" width=\"567\" height=\"265\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-20.png 567w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-20-300x140.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-20-65x30.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-20-225x105.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-20-350x164.png 350w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">Fig 3: Principle of measuring mass via decay counting method.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>2.3.1.2 Essential components : <\/strong>A typical AMS system essentially includes the following:<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-56 size-full aligncenter\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-21.png\" alt=\"\" width=\"689\" height=\"225\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-21.png 689w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-21-300x98.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-21-65x21.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-21-225x73.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-21-350x114.png 350w\" sizes=\"auto, (max-width: 689px) 100vw, 689px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">Fig 4: Schematic diagram showing essential components of a mass spectrometer.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Ion source : <\/strong>The sample material containing the rare isotopes to be counted is placed in the ion source. The neutral atoms are converted into the negatively charged ions. This is required because all mass spectrometers use E.M. fields to manipulate atoms and the atoms must be charged (and hence be ions) to be manipulated. The AMS systems based on tandem electrostatic accelerators employ ion sources which utilize a beam of Cs+ ions to sputter material from the sample. The ion source also provides some degree of focusing, collimation &amp; acceleration to ions. Most mass spectrometers use positive ions, since they are in general more easily created, but sometimes using negative ions is required.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">Mass Analyzer : <\/strong><span style=\"text-align: initial; font-size: 1em;\">is a filter that separates ions by mass (or more specifically by momentum or energy) in space or in time by using a combination of electric and magnetic fields (RF fields). It also <\/span>provide<span style=\"text-align: initial; font-size: 1em;\"> some degree of focusing to compensate for any optical spread of the ion beam leaving the source. <\/span>Usually<span style=\"text-align: initial; font-size: 1em;\"> the choice of mass separator &amp; ion source is guided by the following parameters : (a) sample character, i.e. is the sample a gas, liquid, solid&amp; in what state of purity? (b) The abundance of <\/span>isotope<span style=\"text-align: initial; font-size: 1em;\"> in the material, i.e. how abundant is the material? Is it common or trace? (c) isotopic abundance, i.e. are the isotopes of interest all of <\/span>similar<span style=\"text-align: initial; font-size: 1em;\"> abundance, or are they drastically different? (d) <\/span>range<span style=\"text-align: initial; font-size: 1em;\"> of variation, i.e. do the isotope ratios vary a lot or a little? ( e) Are there any interferences, i.e. are there isotopes of another element or compounds\/isotopes of similar m\/e (mass to charge ratio) that must be eliminated or separated? (f) our requirement, i.e. whether absolute or relative ratios are needed.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">Detector: <\/strong><span style=\"text-align: initial; font-size: 1em;\">The <\/span>iidentification<span style=\"text-align: initial; font-size: 1em;\"> and counting of the individual rare isotopes <\/span>is<span style=\"text-align: initial; font-size: 1em;\"> done with nuclear detection techniques to measure ions leaving mass analyzer. The detection method mostly depends on the ion beam intensity which <\/span>range<span style=\"text-align: initial; font-size: 1em;\"> from a few ions per second to a fraction of a nano-ampere (109-1010 ions per second).<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong style=\"text-align: initial; font-size: 1em;\">Computer controlled data acquisition system : <\/strong><span style=\"text-align: initial; font-size: 1em;\">In order to allow for an unattended operation of the identification process and to provide control of the AMS system parameters, a computer controlled data acquisition system is needed and the live images of the ions collected <\/span>is<span style=\"text-align: initial; font-size: 1em;\"> obtained.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-57 size-full\" src=\"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22.png\" alt=\"\" width=\"806\" height=\"491\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22.png 806w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22-300x183.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22-768x468.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22-65x40.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22-225x137.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-content\/uploads\/sites\/86\/2018\/11\/Untitled-22-350x213.png 350w\" sizes=\"auto, (max-width: 806px) 100vw, 806px\" \/><\/p>\n<p><span style=\"text-align: initial; font-size: 1em;\">problems or, in some cases, itself influence the process being studied. AMS allows very low levels of tracer to be used, completely avoiding these problems.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong style=\"text-align: justify; font-size: 1em;\">2.3.1.4 Limitations of AMS technique : <\/strong><span style=\"text-align: justify; font-size: 1em;\">The serious limitation of AMS is that it tends to be more expensive than decay counting. <\/span>Technique<span style=\"text-align: justify; font-size: 1em;\"> essentially uses an accelerator and purchasing and maintaining a particle accelerator and its associated components <\/span>is<span style=\"text-align: justify; font-size: 1em;\"> expensive.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"font-size: 1em;\">3. Summary:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">The knowledge of basic nuclear properties of nuclei and the ways of measuring them accurately is very important. The charge and mass are fundamental to any nucleus and therefore their accurate determination is essential. The nuclear charge can be measured in a variety of ways with each method have its own advantages and disadvantages. The method of measuring the charge distribution in nuclei with electron scattering method is very useful and give direct access to the nuclear environment. It gives a fairly accurate value of the charge distribution and is therefore considered as the best method so far. To measure the mass of nuclei, though a number of methods are available but owing to its accuracy, less <\/span>time consuming<span style=\"text-align: initial; font-size: 1em;\"> nature and other unique advantages, the accelerator mass spectrometer technique is more useful.<\/span><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n","protected":false},"author":3,"menu_order":2,"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-38","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\/38","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\/38\/revisions"}],"predecessor-version":[{"id":360,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapters\/38\/revisions\/360"}],"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\/38\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/media?parent=38"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/pressbooks\/v2\/chapter-type?post=38"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/contributor?post=38"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/wp-json\/wp\/v2\/license?post=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}