Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.     

Partial level density of n-quasiparticle excitations, radiative strength functions and new experimental information on the dynamics of nuclear structure change in the B n range

The most reliable at present values of the level density in the fixed spin window and the sums of radiative strength functions of cascade gamma transitions are obtained from analysis of intensities of two-step cascades excited upon thermal neutron capture for approximately 40 nuclei in the mass range 40 ≤ A ≤ 200. The maximal reliability of these data is provided by the experimental conditions—minimum possible propagation error coefficients and practically unique solution of the problem of determination of gamma decay parameters from measured spectra. The experimental data are approximated by the sum of partial level densities corresponding to excitation of n quasiparticles. Steplike structures in the level density at excitation energies smaller than 3–4 MeV are described with good accuracy as the superposition of two-quasiparticle (three-quasiparticle in odd A nuclei) and vibrational excitations with the coefficient of collective density enhancement K _coll ≈ 10?20. They correspond to excitation-energy-correlated maximum enhancement of the radiative strength functions of primary gamma transitions. The level density at larger excitation energies is well reproduced if the breakup of at least two more Cooper pairs of nucleons is taken into account. The increase in the number of excited quasiparticles in the nucleus corresponds to unconditional reduction of the radiative strength functions of primary gamma transitions of the compound state decay. However, the maximum possible value of partial widths of primary transitions increases regularly with decreasing energy. Some ambiguity in the results of approximation and divergence from existing theoretical ideas of the energy dependence of nucleon correlation functions in an excited nucleus point to the possibility of direct extraction from experiment of fundamentally new information on the structure of excited nuclear levels in the range of the neutron binding energy. These are, first of all, the parameters of dependence of nucleon correlation functions on the excitation energy of the nucleus.     

New perspectives on the level density of compound resonances

The level density of compound resonances observed at neutron separation energy is subject of closer investigation and interpretation. The structures in the level density parameter as a function of the mass number allow the determination of the hierarchy of the compound states and the definition of a base line which represents the level density parameter of spherical nuclei with no residual interaction and no shell effects. Using the base line a method becomes available enabling the separation of the residual interaction from properties of the average potential defined in the framework of the shell model. The following examples in different mass regions are discussed: the change of the pairing energy due to the blocking effect atA ≈ 70; the breakdown of the pairing correlation atA ≈ 105 is interpreted as neutron-proton interaction; similar effects in the mass region 150<A<170 are discussed with neutron-proton interaction and the backbending phenomen. Finally it will be shown that there is no enhancement of states due to collective properties of nuclei at high excitation energy.     

Damping of collective modes in DIC: Quantal versus statistical fluctuations

A model is developed to describe the transformation of relative kinetic energy into intrinsic excitation energy in DIC. Energy dissipation is viewed as an indirect process, in which collective vibrational modes are first excited coherently and then damped due to the coupling to the remaining non-collective degrees of freedom. Both collective and intrinsic degrees of freedom are included explicitly, and the coupling between them is treated in a random-matrix model. Under certain assumptions it is shown that, in the weak-coupling limit, the collective probability distribution in phase space obeys a Fokker-Planek equation. This transport equation is used to derive equations of motion for the expectation values of some “macroscopic” quantities characterizing the process. Some numerical results are presented and a qualitative comparison with the Copenhagen model is attached.     

Nuclear structure at finite temperature: A review

Information on nuclear structure at finite temperature is obtained from the physics of the level density, of the rotational damping, and of the giant dipole resonance thermally excited on a compound nucleus at very large excitation energy (and angular momentum). The current understanding in terms of mean-field theories and beyond is reviewed. The coupling to doorway states and the coupling to many-particle-many-hole states in the random-matrix-theory limit are discussed. Emph asis will be on the close relation between the single-particle damping and the damping of collective vibrations. The coherence between the particle and the hole strongly suppresses the vibrational damping, in particular, the temperature dependence.     

Level densities of heaviest nuclei

The intrinsic level densities of superheavy nuclei in the α-decay chains of ^296,298,300120 are calculated using the single-particle spectra obtained with the modified two-center shell model. The role of the shell and pairing effects on the level density as well as their quenching with excitation energy are studied. The extracted level density parameter is expressed as a function of mass number, ground-state shell correction, and excitation energy. The results are compared with the phenomenological values of level density parameters used to calculate the survival of excited heavy nuclei.     

The adiabatic approximation as a diagnostic tool for torsion-vibration dynamics

The adiabatic separation of large-amplitude torsional motion from small-amplitude vibrations is applied as an aid in interpreting the results of fully coupled quantum calculations on a model methanol Hamiltonian. Comparison is made with prior work on nitromethane [D. Cavagnat, L. Lespade, J. Chem. Phys. 106 (1997) 7946]. Even though the torsional potentials are very different, both molecules show a transition from adiabatic to diabatic behavior when the CH stretch is excited to ν_CH = 4 or higher. In the adiabatic approximation, the effective torsional potentials for the various CH stretch vibrational states do not cross, but the CH vibrational amplitude moves from one bond to the next as a function of torsional angle. In the diabatic approximation, the effective torsional potentials do cross, but the distribution of the CH vibrational amplitude remains approximately constant in the vicinity of the crossing. The transition to diabatic behavior is promoted by the normal mode to local mode transition, and the relevant adiabatic and diabatic effective torsional potentials are determined by the torsion-vibration coupling. The torsion-vibration couplings in the four overtone manifolds considered (methanol OH, CH, nitromethane CH, and hydrogen peroxide OH) are large, reaching 265-500 cm⁻¹ by ν_XH = 6, and are of generally similar magnitude. The largest torsion-vibration couplings involve the first Fourier term in the torsional angle (cosγ for the CH stretch in methanol and the OH stretch in HOOH), whereas higher Fourier terms (cos2γ in nitromethane and cos3γ for the OH stretch of methanol) result in somewhat weaker coupling. Nonadiabatic matrix elements in methanol couple the torsional and vibrational energies and they exhibit a slow fall-off with coupling order.     

Role of Mode-mode Coupling in Short-time Excited State Decay

Master equation of a relevant electronic and vibrational system is derived for a special diabatic basis corresponding to vertical processes. It is shown that bath modes contribute dynamically to the inter-state coupling only at short times. For long times the bath-induced inter-state coupling is static and increases with the contribution of bath modes to the Stokes shift and to the Herzberg-Teller correction of the excited state. Simultaneously, the time evolution of excited state population is studied numerically for the system consisting of two electronic levels interacting with two vibrational modes, coupled to a heat bath. A mutual coupling of the vibrational modes in the excited state is taken into account (Duschinsky effect). Excited state population relaxes faster if interacting vibrational mode dissipates its energy via vibrational mode of a smaller eigenfrequency. Fast component of excited state depopulation cannot be achieved via coherent mode-mode coupling, if the second mode is not directly coupled to the electronic inter-state transition.     

Level densities in the Pairing plus Quadrupole model for Erbium isotopes

The level densities, up to about 100 MeV of excitation energy, for even Erbium isotopes are computed using the Pairing plus Quadrupole model, in the framework of the Static Path Approximation (SPA). The resulting level densities are in reasonable agreement with the empiricalA/8 law below 40 MeV of excitation energy. At higher excitation energies (U?60 MeV) the level densities agree with the Fermi gas formula witha?A/10. The inclusion of small amplitude collective motion (RPA-SPA) does not improve the results over the SPA at high excitation energy, and gives small corrections to the ground state energy.     

The excitation of collective nuclear states by high energy particles

The excitation of collective nuclear states by high energy particles is considered within the framework of the Glauber theory. The approach is based on the adiabatic approximation and expansion of the scattering amplitude in powers of the nonsphericity parameter. The formulae for the excitation cross sections of the rotational and one- and two-phonon vibrational states, as well as the elastic scattering cross section with the collective motion included, are obtained. The effect of nucleon correlations in both elastic and inelastic cross sections is also studied. The theoretical predictions are compared to new data on 1 GeV proton scattering by ⁵⁸Ni, ²⁰⁸Pb, ¹²C, ⁴⁰Ca and ³⁹K. A comparison with electron scattering data is simultaneously carried out. The agreement with the experimental data is generally good.     

CO dynamics induced by tunneling electrons: differences on Cu(110) and Ag(110)

The electronic current originating in a scanning tunneling microscope (STM) can be used to induce motion and desorption of adsorbates on surfaces. The manipulation of CO molecules on noble metal surfaces is an academic case that has received little theoretical attention. Here, we do thorough density functional theory calculations that explore the chemisorption of CO on Cu(110) and Ag(110) surface and its vibrational properties. The STM induced dynamics are explored after excitation of the highest lying mode, the C–O stretch. In order to give a complete account of this dynamics, the lifetime of the different CO modes is evaluated (by only including the mode decay into electronic excitations of the host surface) as well as the intermode coupling. Hence, after excitation of the stretch mode, the lower-energy modes are populated via intermode coupling and depopulated by electron-hole excitations. This study reveals the intrinsic features of the STM induced motion of CO on Cu(110) and Ag(110).     

Threshold dependence of the vibrational excitation of molecules on laser radiation intensity

The collisionless vibrational excitation of a polyatomic molecule in an IR laser radiation field has been theoretically studied. It has been shown that (i) the degree of vibrational excitation (namely, number 0000 of vibrational quanta of a molecular mode near-resonant with the IR laser field that are absorbed by the molecule) is low if laser pulse intensity P (energy flux density in the laser beam) is lower than a certain critical value P _cr; (ii) the degree of excitation abruptly increases after crossing the boundary where P = P _cr; (iii) this effect is attributed to two properties inherent in polyatomic molecules, namely, the anharmonicity of the vibrational mode interacting with the laser field and the energy exchange with other modes; and (iv) at P > P _cr, number 00000 is determined only by energy density Φ = Pτ_P, where τ_P is the laser pulse duration, 00000 monotonically increases with increasing Φ. The model is in good agreement with the experimental data.     

Electromagnetic transition rates and vibrational modes in34S

States in³⁴S up to 6 MeV excitation energy, populated by the reaction³¹P(α, pγ), have been investigated by Doppler shift and line shape analysis andpγ andγγ angular correlation measurements. The strengths of electromagnetic transitions between even parity levels are compared with theoretical predictions of the weak coupling unified model and the many-particle shell model. The experimental evidence for a weak coupling of the single particle motion to vibrational modes is discussed.     

Vibrational kinetics of the active media of CW CO<Subscript>2</Subscript> lasers

The vibrational kinetics of CW CO₂ lasers has been analyzed within the framework of a temperature model. The necessity of taking into account the coupling of the vibrational modes of the CO₂ molecule in determining the occupation numbers and the store of vibrational energy in individual modes is shown. Expressions that connect vibrational temperatures with the rates of excitation and relaxation of the lower vibrational levels of modes have been obtained. The ratios between the vibrational temperatures on selective excitation of the 00° 1 level and on excitation of CO₂ molecules in an electric discharge as well as the character of the dependences of vibrational temperatures on the pumping-energy value are discussed.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 72–79, January–February, 2005.     

Cascade γ decay of the 191Os compound state

The intensities of two-step cascades to the final levels with excitation energies below 0.82 MeV have been determined from the accumulated experimental data on the γ-γ coincidences at thermal neutron capture into ¹⁹⁰Os. These intensities made it possible to establish the decay scheme for the compound nucleus to excitation energies of about 3 MeV. The intervals of the level densities and sums of radiative strength functions of the E1 and M1 transitions, which exactly reproduce the experimental cascade intensities, have been found from the total cascade intensities. The level density is approximated by the sum of the partial densities of levels for different numbers n of quasiparticles, with the coefficient of collective increase in the density, unambiguously determined by the accepted concepts about the energy dependence of the correlation functions of the nucleons of an excited nucleus.     

The level structure of 189Os

The level structure of ¹⁸⁹Os has been studied by (d, p), (d, t) and (d, d') reaction spectroscopy at E_d = 12.1 MeV. Assignments of a number of levels at excitation energies below ≈ 1700 keV are given. The assignments are discussed in terms of a unified model based on the Nilsson model including pairing, rotational motion and attenuated Coriolis coupling. Deviations between predicted and experimental excitation energies and wave functions are generally found to be consistent with trends observed in ¹⁸⁷Os and in the odd W isotopes. Evidence for the existence of collective non-rotational states is found from the (d, d') reactions. Results of (³He, α) and high resolution γ-ray and conversion electron studies were also included at various stages of the investigation to supplement the data from the deuteron induced reactions. Comparisons between calculated and measured B(E2) values are found to indicate an intrinsic quadrupole moment of the ground-state band of ≈ 5.0 b, in agreement with values in adjacent even Os isotopes. Details of the Coriolis coupling calculations are given.     

Influence of particle number fluctuations and vibrational modes on thermodynamic characteristics of a hot nucleus

Nogami's method is extended to finite temperatureT. The effect of quantum and statistical fluctuations for the particle number in the finite temperature BCS model on the excitation energy, entropy, specific heat, level density and level density parameter is calculated in hot⁵⁸Ni nucleus. The calculations have been performed with the finite temperature BCS gap and statistical average gap due to the finiteness of nucleus. In the finite temperature RPA the contribution of dipole and quadrupole vibrational modes to the specific heat and the increase of level density is calculated.     

Thermal source parameters in Au+Au central collisions at 35 A MeV

Central Au+Au collisions at 35 A MeV are analyzed to find the characteristics of a thermal source, in the framework of the statistical multifragmentation model SMM. A recently introduced backtracing protocol provides an effective comparison of theory and experiment. For the first time the distributions of the central source parameters (density, mass number, excitation energy) are found. The collective energy of primary fragments is also deduced. It is shown that the backtracing procedure allows an estimation of the pre-equilibrium emission.