Measurement of the Damping of the Nuclear Shell Effect in the Doubly MagicPb208Region

Abstract

The damping of the nuclear shell effect with excitation energy has been measured through an analysis of the neutron spectra following the triton transfer in the 7 Li induced reaction on 205 Tl.The measured neutron spectra demonstrate the expected large shell correction energy for the nuclei in the vicinity of doubly magic 208 Pb and a small value around 184 W. A quantitative extraction of the allowed values of the damping parameter γ, along with those for the asymptotic nuclear level density parameterã, has been made for the first time. The shell effect is a cornerstone of the mean field theory describing finite fermionic systems. The shell structure in atoms decides the chemical properties of the corresponding elements. In nuclear physics the spin orbit coupling, in addition, plays a dominant role in deciding the shell closures and the associated magic numbers of protons and neutrons. The nuclei having such numbers of neutrons and protons have an extra stability with respect to that expected from the average behaviour described by the liquid drop model (LDM). Many important nuclear phenomena such as the occurrence of super heavy elements [1,2], fission isomers [3,4], super-deformed nuclei [5] and new magic numbers in exotic nuclei [6,7] are the consequences of the shell effect. The shell effect also affects another fundamental property of the nucleus viz. the nuclear level density (NLD). The NLD is an indispensable input to the statistical calculation of compound nuclear decay and thus an important physical quantity for many practical applications, such as the calculations of reaction rates relevant to nuclear astrophysics, nuclear reactors and spallation neutron sources.The NLD was first calculated by Bethe using a noninteracting Fermi gas model, without shell effects, arriving at its leading dependence on excitation energy (E X ) and angular momentum (J) [8,9]. The generic behaviour with respect to E X is described by e 2 √ aE X . Here 'a' is the NLD parameter which is related to the single particle density at the Fermi energy. Direct measurements of the NLD are based on the study of slow neutron resonances, which are mainly s-and p-wave, and are extrapolated to higher J values to estimate the angular momentum summed or total NLD. The total NLD inferred from such a measurement shows that on the average the level density parameter a increases linearly with the mass number (A) of the nucleus as a ≈A/8 MeV −1 . However, there is a significant departure from this liquid drop value at shell closures. This departure is the largest for the doubly magic nucleus 208 Pb, where a (at E X ∼7 MeV) is as low as A/26 MeV −1 . This shell effect on the NLD parameter is expected to damp with excitation energy so that a approaches its liquid drop value at E X ∼ 40 MeV [10]. It is important to make measurements on the damping of the shell effect over a wide E X range. To our knowledge, no such measurement has been reported.Experimental information on the damping of the shell effect can be obtained by measuring the E X dependence...

Fission barrier, damping of shell correction, and neutron emission in the fission ofA∼200

“…[15], the calculated neutron mean life and hance the extracted fission delay also depends on the value of level density parameter. In the above calculation the value ofã n is assumed to be A/9, which gave a better reproduction of the experimental partial xn excitation functions [14] and is also within the acceptable range of A/8 to A/9.5, determined from the measured neutron spectrum for a nearby compound nucleus ( 208 Pb) [34]. Significant near scission emission (0.1 -0.3 neutrons/fission) has been reported in spontaneous and induced fission at low energies of actinide nuclei in the literature [35].…”

Synthesis of superheavy elements: Uncertainty analysis to improve the predictive power of reaction models

“…It can be seen that the chosen range of β can accommodate most of the extracted values. As regards the shell-damping energy E d , typical values can be found in some recent papers [42,47], which demonstrate the chosen range of values. Accordingly, the default values of the above two parameters are taken to be 5.0 zs −1 and 19.0 MeV, namely their mean values.…”

“…In our case, for example, the reduced friction coefficient and the shell-damping energy cannot be determined with certainty [38,[40][41][42]. Hence, one needs to construct some input probability distributions for them.…”

“…As its name indicates, such ranges are able to cover most of values that can be found in the literature [38,[40][41][42][43][44][45][46], but the associated uncertainties appear quite large. To justify this choice, Fig.…”

Ignatyuk damping factor: A semiclassical formula

“…The damping coefficient γ, has no known exact expression and is often employed as a fitting parameter. It has the typical value between 0.04 to 0.07 MeV −1 (see for example, [17]).…”