ROLE OF ISOSPIN IN HEAVY AND NEUTRON-RICH NUCLEI

Abstract

Isospin is an established concept and has been playing a very fundamental role in particle physics. However, its applications to nuclear physics have been largely restricted to light mass nuclei and certain decay modes only. This thesis is concerned with the concept of isospin quantum number, its possible conservation in heavy mass nuclei and some empirical evidences supporting the same. It, therefore, revives an old debate about the applicability of isospin in heavy nuclei. Isospin was rst introduced by Heisenberg in 1932 [1] to make a distinction be- tween neutrons and protons in the absence of electromagnetic interactions. The protons and neutrons were considered to be the different projection states of the same particle called a \nucleon". Soon, isospin became an important and useful concept both from nuclear structure and reaction point of view. In technical terms, isospin was introduced as a third coordinate in nuclear wave function along with the space and spin coordinates to generalize the Pauli exclusion principle as proposed by Cassen and Condon [2]. Wigner in 1937 [3] discussed the possible consequences of the symmetry of nuclear forces i.e. equality of forces between nn, pp and np pairs. This suggested that isospin is a reasonably good quantum number and it can be used to label the members of an isobaric multiplet (A group of states in neighboring isobars). However, in the presence of Coulomb forces, isospin ceases to be a good quantum i ii number because of mixing with states having higher isospin values. Many different models have been used to calculate the isospin mixing like the shell model, Fermi gas model, hydrodynamical model, and microscopic models etc. Lane and Soper [4] were the rst to predict on the basis of the Fermi gas model calculations that isospin purity increases as we move towards heavy nuclei with neutron excess, N > Z. We provide empirical evidences for this concept in our work in two different ways. In the rst approach, we calculate the relative yields of ssion fragments emitted in heavy ion induced fusion- ssion reactions, 208Pb(18O, f) and 238U(18O, f). Since the nuclei involved in these reactions are heavy nuclei having N > Z, we assume that isospin is a good quantum number and remains reasonably conserved during ssion. We are able to reproduce the gross features of the ssion fragment distribution reasonably well, con rming the validity of isospin quantum number. We, further, consider the thermal neutron-induced ssion, 245Cm(nth, f) and apply the same methodology to reproduce the ssion fragment distribution with reasonable accuracy, again con rm- ing the validity and goodness of isospin. In the second approach, we look for isospin dependence of ssion decay widths in heavy nuclei, again considering isospin con- servation in ssion. The results from both the approaches favor the idea of isospin purity in N > Z nuclei. In Chapter 1, we present a brief historical overview of isospin. After introduc- ing the basics of isospin, we discuss the selection rules of isospin for various decay processes like -decay, and -decay [5{8]. The basic algebra and selection rules for isospin are discussed in detail in the review articles of Robson [9] and Temmer [10]. A major breakthrough in the history of isospin came with the discovery of Isobaric Ana- log States (IAS) in light and medium mass nuclei [11{14]. Isobaric analog states are the states which exist in neighboring isobars and have same isospin, spin and parity and also lie at same energy provided charge independence of nuclear forces holds. IAS can, therefore, be used to test the charge independence and charge symmetry [15,16] of nuclear forces. In Chapter 2, we discuss the various approaches to calculate isospin impurity iii in nuclear states. Isospin mixing was rst calculated by MacDonald [17] using Fermi gas model. It was calculated for even-even N = Z light nuclei. Lane and Soper [4] further extended this approach to calculate the isospin impurity in heavy nuclei and showed that mixing of isospin with one unit higher isospin state decreases by a factor of 2=(N􀀀Z+2). Thus, isospin appears to become increasingly good quantum number with the rise in the neutron excess. Further calculations were carried out by using the shell model [18, 19]. Sliv and Kharitonov calculated the isospin mixing along -stability line using the shell model [19]. They found that isospin mixing rst rises up to 7% for 40Ca and then starts decreasing as we move along the -stability line, reaching to 2% for 208Pb which is same as that for light nuclei. Hydrodynamical model calculations for isospin mixing are discussed by Bohr et al. [20] with similar results supporting the idea that isospin mixing decreases with the increase in neutron number. Auerbach [21] in his review has compared the isospin mixing using various approaches like the shell model, hydrodynamical model, energy weighted sum rule, non-energy weighted sum rule, Hartree-Fock method, RPA etc. The RPA approach was considered to be the most reliable and gives a very small isospin purity in nuclei with excess neutrons. It may be safely concluded on the basis of all the theoretical calculations that isospin mixing decreases with the neutron excess as we move towards heavy nuclei. Therefore, this may be considered as a reasonably good quantum number in the heavy nuclei having N > Z and also in the neutron-rich nuclei. In Chapter 3, we use the concept of isospin conservation in heavy ion induced ssion to calculate the relative yields of fragments formed in compound nucleus ssion. We have only three sets of experimental data [22{24] where measurement of fragment data are known to the precision of one unit in Z and A and partition wise ssion fragment mass distribution are also known. The rst two data sets belong to the 208Pb(18O, f) reaction and the third data set belongs to the 238U(18O, f) reaction. Both the reactions have targets with neutron excess, N > Z which makes them ideal to test isospin purity. We use isospin conservation to assign isospin values to the various nuclei involved in ssion. We also use Kelson's arguments which we term as Kelson's iv conjectures [25] to assign isospin to various ssion fragments. Kelson had suggested that the nal ssion fragments are likely to form in IAS. We also use the experimental neutron multiplicity data to obtain weight factors for various n-emission channels, if available. For 208Pb(18O, f) reaction, we use data from Bogachev et al. [22] which has given the full neutron multiplicity data for each partition separately. Therefore, we are able to calculate both partition wise and total ssion fragment mass distribution. However, for 238U(18O, f), we know only dominating n-emission channels. This allows us to calculate only partition wise ssion fragment distribution since we do not know which partition will dominate over the others which ultimately leads to symmetric or asymmetric mass distribution. A good agreement between the calculated and the experimental data for both the reactions provides the rst direct evidence for purity of isospin in neutron-rich nuclei and also supports isospin conservation in ssion [26{29]. However, there are deviations at few places which may be due to the shell effects, presence of isomers etc. which we could not consider in our calculations. In Chapter 4, we apply the concept of isospin conservation to thermal neutron induced ssion, 245Cm(nth, f). Here we have only one set of experimental data due to Rochman et al. [30]. We again use Kelson's conjectures to assign isospin to var- ious ssion fragments emitted in all the nine observed partitions. For this case, the neutron multiplicity data are not available. F. Gonnenwein [31] suggests the aver- age neutron multiplicity to be 3.83 for this reaction. Therefore, we have done the calculations with two sets of combinations for n-emission channels: 2n, 4n, 6n and 4n, 6n, 8n. We calculate the relative yields of fragments emitted in all the nine partitions. There is a reasonable agreement between the calculated and experimental data. Since the experimental data exist only for the light mass fragments, we have also made predictions for the heavy mass fragment distribution. We, further, make a prediction for the most symmetric partition Cd-Cd for which experimental data are not available [32]. This proves the isospin conservation to be a useful concept in ssion. In Chapter 5, we provide a different kind of evidence of isospin purity in heavy v nuclei and show that it plays an important role in ssion. Here, we look for the isospin dependence in ssion decay widths. The idea was rst proposed by Yadrovky in 1975 [33]. Yadrovsky considered two reactions, 209Bi(p, f) and 206Pb( , f), both leading to same compound nucleus (CN) 210Po. In proton induced ssion, CN is formed in two isospin states and in alpha induced ssion, there is only one isospin state possible for CN from isospin conservation. The ssion decay widths from two isospin states of CN were calculated and a large difference between the two lead Yadrovsky to conclude that \the compound nucleus remembers the isospin of the states leading to ssion". There can be many other combinations of projectiles leading to same CN but in different isospin states like proton and deuteron, 3He and . However, there are three pairs of reactions for which experimental data of ssion cross-section at different excitation energies are known, where this idea could be tested. We test the idea for these three pairs of reactions, rst is same as considered by Yadrovsky but with new experimental data, second is 185Re(p, f) and 182W( , f), both leading to the CN 186Os and third set is 205Tl(p, f) and 202Hg( , f), both leading to the CN 206Pb. The experimental data of p;f and ;f are taken form Ignatyuk et al. [34] and Moretto et al. [35]. By using the PACE4 results for p and , we calculate the ssion branching ratios from two isospin states of CN. We nd that in all the three cases, the ssion branching ratios from two isospin states are quite different which favors the idea proposed by Yadrovsky that CN somehow remembers the isospin during ssion. Ignatyuk et al. [34, 36] have also reported a difference in the behavior of ssility of the same CN formed in two different reactions, where one is proton induced and the other is alpha induced and highlighted an anomaly noticed in the behavior of the (p, f) and ( , f) cross-sections. The anomaly consisted of higher (p; f) than ( ; f) at lower energies, which reverses the trend at higher energies after a crossing. We use their experimental data of ssility to calculate the ssion branching ratios for the two isospin states in four cases where the compound nucleus 210Po, 209Bi, 207Bi and 198Hg are formed. A similar trend of ssion branching ratios, as observed for the previous three cases, provides a purely empirical evidence of isospin memory in vi CN and further supports our idea that isospin remains conserved in ssion and is a good quantum number in neutron-rich systems. However, our calculations involve CN formation and its decay and thus, it will be valid only up to the point where ssion proceeds by the CN process. After a particular energy, our calculations start showing an unphysical behaviour of ssion branching ratios which we interpret as the rising contribution from non compound processes. This possibly gives a signature of gradual transition to non compound processes with the increase in energy [37, 38]. In Chapter 6, we summarize and conclude the thesis.