Experimental Level Densities Research Articles

The puzzle of suppression of nuclear level density in N ≈ Z Zn isotopes compared to N > Z

A systematic investigation of isospin dependence of nuclear level density (NLD) is performed for the Zn isotopes. Experimental level densities of 67Zn and 61Zn have been determined by analyzing the spectra of evaporated neutrons emitted from the excited 68Zn and 62Zn nuclei populated via 4He + 64Ni and 4He + 58Ni reactions, respectively. At the low excitation energies, the neutron spectra are predominantly contributed by the first-chance decay, leading to 67Zn and 61Zn as daughters for the two cases. A comparison of the present experimental data along with previously measured NLDs of 66Zn, 64Zn, and 60Zn is performed with state-of-the-art microscopic calculations. While the experimental NLDs of stable isotopes (i.e., 67Zn, 66Zn, and 64Zn) align excellently with theoretical predictions, a compelling contrast emerges for the unstable isotopes 61Zn and 60Zn, exhibiting NLDs an order of magnitude lower than predicted. The possible origins of the observed suppression of NLDs for the N ≈ Z isotopes are discussed. A significant reduction of level density for nuclei situated away from the stability line could have critical implications for the calculation of astrophysical reaction rates pertinent to heavy-element nucleosynthesis.

Systematic investigation on semi-empirical thermodynamic quantities of excited nuclei using canonical ensemble

Semi-empirical thermodynamic quantities (TQs) of 78 nuclei ranging from 43Sc to 243Pu have been systematically investigated in the temperature region below 1 MeV using the thermodynamic canonical ensemble. The latter is carried out by taking into account the experimental nuclear level density (NLD) data measured using the Oslo method for the low-excitation region below the neutron binding energy B n combining with the back-shifted Fermi gas NLD model for the excitation energy from B n to about 250 MeV. In particular, the uncertainty of the TQs propagating from the fluctuation of the experimental NLD data has been, for the first time, calculated. The results obtained indicate that the uncertainty of TQs due to the experimental NLD is incomparable with the changes caused by the nuclear structure effects. The free energy of even–even nuclei behaves differently from that of odd-A ones. The total energy in the low-temperature region below T E ≃ 0.4 − 0.6 MeV for medium-mass nuclei and T E ≃ 0.2 − 0.4 MeV for heavy-mass ones slowly varies. When temperature is from T E to 1 MeV, the total energy increases extremely faster than the increase of temperature, exhibiting the constant-temperature behavior. The entropy exhibits an abrupt change in their slope at T S ≃ 0.2 − 0.4 MeV in medium-mass nuclei and T S ≃ 0.5 − 0.6 MeV in heavy-mass ones. The existence of T E and T S has been interpreted due to the breaking of the first Cooper pair. Finally, the heat capacity shows a strongly pronounced S-shape in nuclei belonging to the rare-earth region. The temperatures defined at the center of the S − shaped heat capacities, which are known to closely relate to the critical temperature of the pairing phase transition T C, are quite close to those theoretically predicted, namely T C ≈ 0.5Δ − 0.6Δ with Δ = 12A −1/2 being the empirical pairing gap at zero temperature. The semi-empirical TQs obtained in the present work can be, therefore, a reliable data source to test and/or validate many nuclear thermodynamical models and to examine some nuclear structure properties such as pairing and deformation.

Updated heat capacities of \(^{161-164}\)Dy nuclei

This work presents the updated heat capacities of \(^{161-164}\)Dy nuclei in the nuclear temperature region from 0 to 1 MeV. The updated heat capacities are obtained within the canonical ensemble method making use of the most recent and recommended experimental nuclear level density (NLD) data together with those calculated within the back-shifted Fermi gas (BSFG) model with energy-dependent parameters. By comparing the updated heat capacities with the un-updated ones, which are obtained by using the old experimental NLD data and the BSFG with energy-independent parameters, we found that the updated and un-updated heat capacities are almost identical at low temperature, but differ from each others at high temperature. This discrepancy can be interpreted by the damping of nuclear shell structure with increasing the excitation energy. Besides, we observe that the S-shape in the updated heat capacities is much more pronounced in even-even Dy isotopes than in even-odd ones, whereas the un-updated heat capacities do not clearly exhibit this S-shape. Therefore, the updated heat capacities should provide a more convincing evidence for the signature of pairing phase transition in nuclear systems.

Nuclear level density and thermal properties of $$^{115}\hbox {Sn}$$ from neutron evaporation

The nuclear level density of $^{115}$Sn has been measured in an excitation energy range of $\sim $2 - 9 MeV using the experimental neutron evaporation spectra from the $^{115}$In($p,n$)$^{115}$Sn reaction. The experimental level densities were compared with the microscopic Hartree-Fock BCS (HFBCS), Hartree-Fock-Bogoliubov plus combinatorial (HFB+C), and an exact pairing plus independent particle model (EP+IPM) calculations. It is observed that the EP+IPM provides the most accurate description of the experimental data. The thermal properties (entropy and temperature) of $^{115}$Sn have been investigated from the measured level densities. The experimental temperature profile as well as the calculated heat capacity show distinct signatures of a transition from the strongly-paired nucleonic phase to the weakly paired one in this nucleus.

Systematic of critical temperature of nuclear pairing transition

The critical temperature of nuclear pairing transition has been determined for 440 nuclei between 10Be and 253Cf within a microscopic model. The shell effect and mass number dependence of the critical temperature have been studied. The relation between the pairing gaps of neutrons and protons at zero temperature, and the critical temperature have been investigated. The critical temperatures have been compared with the constant temperatures extracted from the experimental nuclear level densities within a phenomenological model. The comparison shows that our theoretical calculations are consistent with the experimental evidences of pairing transition in nuclei.

Level density and thermodynamics in the hot rotating Tc96 nucleus

Evaporated neutron energy spectra have been measured in coincidence with low-energy discrete $\ensuremath{\gamma}$ rays in the reaction $^{4}\mathrm{He}+^{93}\mathrm{Nb}$ at $E(^{4}\mathrm{He})=28$ MeV. The low-energy light-ion beam provides the scope of extracting the experimental nuclear level density (NLD) in the compound nuclear reaction. Angular-momentum gated NLDs have been extracted in the excitation energy range of ${E}^{*}\ensuremath{\sim}5--15$ MeV from the measured neutron energy spectra. The extracted NLDs have been compared with different theoretical calculations such as the exact pairing plus independent particle model at finite temperature (EP+IPM), Hartree-Fock plus BCS (HFBCS), and Hartree-Fock-Bogoliubov plus combinatorial method (HFBC). Interestingly, the experimental NLDs are in good agreement with the results of the EP+IPM, whereas the HFBCS and HFBC fail to describe these data. Consequently, the thermodynamic properties of $^{96}\mathrm{Tc}$ at finite angular momentum have been extracted using the EP+IPM NLDs. Through the analysis of the calculated thermodynamic quantities, it is shown that no pronounced bump is seen in the heat capacity of $^{96}\mathrm{Tc}$, in opposition with the earlier results of $^{96}\mathrm{Mo}$, which showed a prominent bump at $T\ensuremath{\sim}0.7--1$ MeV. This difference is understandable since pairing in the even-even system ($^{96}\mathrm{Mo}$) is always stronger than that in the odd-odd one ($^{96}\mathrm{Tc}$).

Thermal properties of the Tin odd isotopes 117,119,121Sn

We propose to study the thermal properties of the odd isotopes of Tin: [Formula: see text]Sn. To this end, one used two methods to evaluate the properties of these elements. The first theoretical consideration uses a simple prescription to perform the calculation of these properties based on those of even–even neighboring isotopes, assuming the quasi-particle entropy extensivity. The even–even elements are treated as part of the Modified Lipkin–Nogami (MLN) method that allows to take into account the quantal and statistical fluctuations. The second theoretical approach consists of the generalization of the MLN formalism in the case of odd systems, by using the blocking technique. Then, this approach is applied to evaluate the thermal properties of the considered elements. The obtained results by both theoretical approaches are compared to the experimental data. The latter are deduced from the experimental level density within the canonical ensemble. It appears that the assumption of quasi-particle entropy extensivity at low excitation energy allows a simple and an effective treatment of thermal properties of odd nuclei. Indeed, this approach allows to give a good reproduction of experimental data in the particular in the region where the pairing transition occurs.

Experimental First Order Pairing Phase Transition in Atomic Nuclei

The natural log of experimental nuclear level densities at low energy is linear with energy. This can be interpreted in terms of a nearly 1st order phase transition from a superfluid to an ideal gas of quasi particles. The transition temperature coincides with the BCS critical temperature and yields gap parameters in good agreement with the values extracted from even- odd mass differences from rotational states. This converging evidence supports the relevance of the BCS theory to atomic nuclei.

Observation of low-lying resonances in the quasicontinuum of195,196Pt and enhanced astrophysical reaction rates

An excess of strength on the low-energy tail of the giant dipole resonance recently has been observed in the γ-decay from the quasicontinuum of 195,196 Pt. The nature of this phenomenon is not yet fully investigated. If this feature is present also in the γ-ray strength of the neutron-rich isotopes, it can affect the neutron-capture reactions involved in the formation of heavy-elements in stellar nucleosynthesis. The experimental level density and γ-ray strength function of 195,196 Pt are presented together with preliminary calculations of the corresponding neutron-capture cross sections.

Experimental differential cross sections, level densities, and spin cutoffs as a testing ground for nuclear reaction codes

Proton double-differential cross sections from 59Co(α,p)62Ni, 57Fe(α,p)60Co, 56Fe(7Li,p)62Ni, and 55Mn(6Li,p)60Co reactions have been measured with 21-MeV α and 15-MeV lithium beams. Cross sections have been compared against calculations with the empire reaction code. Different input level density models have been tested. It was found that the Gilbert and Cameron [A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43, 1446 (1965)] level density model is best to reproduce experimental data. Level densities and spin cutoff parameters for 62Ni and 60Co above the excitation energy range of discrete levels (in continuum) have been obtained with a Monte Carlo technique. Furthermore, excitation energy dependencies were found to be inconsistent with the Fermi-gas model.

Role of neutrons and protons in entropy, spin cut off parameters, and moments of inertia

The nuclear level densities, spin cut off parameters, and entropies have been extracted in ${}^{116\ensuremath{-}119}$Sn and ${}^{162,163}$Dy nuclei using superconducting theory, which includes nuclear pairing interaction. The results agree well with the recent data obtained from experimental level densities by the Oslo group for these nuclei. Also, the entropy excess ratio proposed by Razavi et al. [R. Razavi, A.N. Behkami, S. Mohammadi, and M. Gholami, Phys. Rev. C 86, 047303 (2012)] for a proton and neutron as a function of nuclear temperature have been evaluated and are compared with the spin cut off excess ratio. The role of the neutron (proton) system is well determined by the entropy excess ratio as well as the spin cut off excess ratio. The moment of inertia for even-odd and even-even nuclei are also compared. The moment of inertia carried by a single hole is smaller than the single particle moment of inertia.

Spectroscopic Study of63Ni via Cold Neutron Capture Reaction: I. Nuclear Structure of63Ni

The γ-radiation has been investigated for 63 Ni produced by cold neutron capture in an enriched 62 Ni sample. The 315 γ-rays produced were placed in a 63 Ni level scheme, in which 272 placements are new. We determined the excitation energies with 0.2–0.8 keV error and the branching ratios of 62 bound levels in 63 Ni, including 30 new levels. The Q -value of the 62 Ni( n ,γ) 63 Ni reaction amounts to 6837.75±0.18 keV. A large-scale shell-model calculation was performed that included the four single-particle orbits of 0 f 7/2 , 1 p 3/2 , 0 f 5/2 , and 1 p 1/2 , assuming an inert 40 Ca core for negative-parity states, and those of 1 p 3/2 , 0 f 5/2 , 1 p 1/2 , and 0 g 9/2 , assuming a 56 Ni core for positive-parity states. The energies of the low-lying 63 Ni states were successfully reproduced. A mean-field statistical-model calculation was also performed by using a self-consistent interaction between the Hartree–Fock + Bardeen–Cooper–Schrieffer method and the statistical calculation. The calculation result is consistent with the experimental level density of 63 Ni.

Level studies of 71 Ge via 71 Ga (P, nγ) 71 Ge reaction and density of discrete levels in 71 Ge

The excited states of 71Ge have been investigated via the 71Ga (P, n) 71Ge reaction with the proton beam energies from 2.5 to 4.3 MeV. The parameters of the nuclear level density formula have been determined from the extensive and complete level scheme for 71Ge. The Bethe formula for the back-shifted Fermi gas model and the constant temperature model are compared with the experimental level densities. Key words: Level schemes of 71Ge, 71Ga (P, n) 71Ge reaction, angular distribution, Fermi gas model.

Level studies of 93Mo via 93Nb(p, nγ)93Mo reaction and density of discrete levels in 93Mo

The excited states of 93Mo have been investigated via the 93Nb(P,n?)93Mo reaction with proton beam energies of 2.5-4.3 MeV. The parameters of the nuclear level density formula were determined from the extensive and complete level scheme of 93Mo. The Bethe formula for the back-shifted Fermi gas model and the constant temperature model are compared with experimental level densities.

Thermodynamic properties of hot nuclei within the self-consistent quasiparticle random-phase approximation

The thermodynamic properties of hot nuclei are described within the canonical and microcanonical ensemble approaches. These approaches are derived based on the solutions of the BCS and self-consistent quasiparticle random-phase approximation at zero temperature embedded into the canonical and microcanonical ensembles. The obtained results agree well with the recent data extracted from experimental level densities by Oslo group for $^{94}$Mo, $^{98}$Mo, $^{162}$Dy and $^{172}$Yb nuclei.

Precise model approximation of JINR (Dubna) data on nuclear level densities in the region 40 ≤ A ≤ 200 below B n

The experimental nuclear level density below the neutron binding energy B n in the mass region 40 ≤ A ≤ 200 is approximated to a high precision on the basis of the Strutinsky model combined with the assumption that the coefficient of collective enhancement of the level density for a given number of excited quasiparticles decreases exponentially with increasing excitation energy. This combination of model concepts makes it possible to reproduce faithfully not only the general trend revealed by the method developed at the Joint Institute for Nuclear Research (JINR, Dubna) in the change in the level density with increasing excitation energy in any nuclei but also the fine structure of this level density. Realistic experimental information about the change in the relationship between the densities of quasiparticle- and vibrational-type states was obtained for the first time for any nuclei virtually up to the neutron binding energy B n .

Level density andγ-decay properties of closed shell Pb nuclei

The level densities and $\ensuremath{\gamma}$-ray strength functions of $^{205\ensuremath{-}208}\mathrm{Pb}$ have been measured with the Oslo method, using the $(^{3}\mathrm{He},^{3}\mathrm{He}{}^{'}\ensuremath{\gamma})$ and $(^{3}\mathrm{He},\ensuremath{\alpha}\ensuremath{\gamma})$ reactions on the target nuclei $^{206}\mathrm{Pb}$ and $^{208}\mathrm{Pb}$. The extracted level densities are consistent with known discrete levels at low excitation energies. The entropies and temperatures in the microcanonical ensemble have been deduced from the experimental level density. An average entropy difference of $\ensuremath{\Delta}S~0.9{k}_{B}$ has been observed between $^{205}\mathrm{Pb}$ and $^{206}\mathrm{Pb}$. The $\ensuremath{\gamma}$-ray strength functions in $^{205\ensuremath{-}208}\mathrm{Pb}$ have been extracted and compared with two models; however, none of them describe the data adequately. Intermediate structures have been observed in the $\ensuremath{\gamma}$-ray strength functions for $\ensuremath{\gamma}$-ray energies below neutron threshold in all the analyzed Pb nuclei. These structures become less pronounced while moving from the doubly magic nucleus $^{208}\mathrm{Pb}$ to $^{205}\mathrm{Pb}$.

Level studies of 73As via 73Ge(p, nγ)73As reaction and density of discrete levels in 73As

The excited states of 73As have been investigated via the 73Ge(p, n?)73As reaction with the proton beam energies from 2.5-4.3 MeV. The parameters of the nuclear level density formula have been determined from the extensive and complete level scheme for 73As. The Bethe formula for the back-shifted Fermi gas model and the constant temperature model are compared with the experimental level densities.

Thermodynamic properties ofFe56,57

Nuclear level densities for $^{56,57}\mathrm{Fe}$ have been extracted from the primary $\ensuremath{\gamma}$-ray spectra using (${}^{3}\mathrm{He}, {}^{3}{\mathrm{He}}^{'}\ensuremath{\gamma}$) and (${}^{3}\mathrm{He}, \ensuremath{\alpha}\ensuremath{\gamma}$) reactions. Nuclear thermodynamic properties for $^{56}\mathrm{Fe}$ and $^{57}\mathrm{Fe}$ are investigated using the experimental level densities. These properties include entropy, Helmholtz free energy, caloric curves, chemical potential, and heat capacity. In particular, the breaking of Cooper pairs and single-quasiparticle entropy are discussed and shown to be important concepts for describing nuclear level density. Microscopic model calculations are performed for level densities of $^{56,57}\mathrm{Fe}$. The experimental and calculated level densities are compared. The average number of broken Cooper pairs and the parity distribution are extracted as a function of excitation energy for $^{56,57}\mathrm{Fe}$ from the model calculations.

Heavy Deformed Nuclei in the Shell Model Monte Carlo Method

We extend the shell model Monte Carlo approach to heavy deformed nuclei using a new proton-neutron formalism. The low excitation energies of such nuclei necessitate low-temperature calculations, for which a stabilization method is implemented in the canonical ensemble. We apply the method to study a well-deformed rare-earth nucleus, 162Dy. The single-particle model space includes the 50-82 shell plus 1f_{7/2} orbital for protons and the 82-126 shell plus 0h_{11/2}, 1g_{9/2} orbitals for neutrons. We show that the spherical shell model reproduces well the rotational character of 162Dy within this model space. We also calculate the level density of 162Dy and find it to be in excellent agreement with the experimental level density, which we extract from several experiments.