Effect of vibrational states on nuclear level density
- PDF / 653,093 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 96 Downloads / 204 Views
NUCLEI Theory
Effect of Vibrational States on Nuclear Level Density* V. A. Plujko** and O. M. Gorbachenko Nuclear Physics Department, Taras Shevchenko National University, Kyiv, Ukraine Received October 31, 2006
Abstract—Simple methods to calculate a vibrational enhancement factor of a nuclear level density with allowance for damping of collective state are considered. The results of the phenomenological approach and the microscopic quasiparticle–phonon model are compared. The practical method of calculation of a vibrational enhancement factor and level density parameters is recommended. PACS numbers: 21.10.Ma, 21.60.Ev, 24.10.Pa, 24.60.Dr DOI: 10.1134/S1063778807090256
1. INTRODUCTION A nuclear level density ρ determines the characteristics of nuclear decay and is one of the basic quantities for description of highly excited nuclear states and analysis of their nature. From a theoretical point of view, the level density is the inverse Laplace transform of the partition function Z({βj }) for an ensemble of canonical distributed states with the “thermodynamic” parameters {βj } (j = 1, ..., k), which are also integration variables in this multidimensional inverse Laplace transformation [1, 2]: ρ(U ) ≡ L−1 {Z({βj })},
(1)
where U is the excitation energy and the symbol L−1 denotes the inverse Laplace transform operator. The number k of parameters βj can coincide with the number of integrals of motion. For simplicity, here and below, we indicate only one argument of level density (the excitation energy U ) but will additionally fix only the number A of nucleons (the corresponding parameters will be denoted as β1 ≡ β and β2 ≡ α, respectively). The collective states can strongly affect the level density, specifically, at low excitation energies (see, e.g., [2–6]). The simplest method to estimate the effect of vibrational states on level densities is to calculate a vibrational enhancement factor Kvibr : Kvibr (U ) = ρ(U )/ρ0 (U ) ≡L ∗ **
−1
{Z({βj })}/L
−1
{Z0 ({βj })}.
The text was submitted by the authors in English. E-mail: [email protected]
(2)
Here, ρ0 (U ) ≡ L−1 {Z0 ({βj })} and ρ(U ) ≡ L−1 {Z({βj })} (Z0 and Z) are level densities (partition functions) without and with allowing for vibrational states, which, in line with the RPA, we regard as conditioned by a residual interaction of a coherent type. At present, there are some unresolved problems in evaluation of this factor. First of all, there is uncertainty in estimating the magnitude of this factor. Different approaches lead to different values of Kvibr . For example, according to the phenomenological closed-form methods [1, 6, 7], one obtains Kvibr (Sn ) ≈ 15–30 near neutron separation energies Sn for nuclei with A ≈ 100. However, Kvibr (Sn ) was found to be equal to 2–5 in microscopic calculations within the quasiparticle–phonon model [2]. It should also be mentioned that changes of Kvibr (U ) with excitation energy strongly depend on the energy behavior of vibrational state damping, which is caused by a noncoherent part of residual interaction. The probl
Data Loading...
