Quasiparticle-phonon Nuclear Model Research Articles

Description of radiative strength functions in deformed nuclei

Radiative strength functions ofE1- andM1-transitions from ground states of doubly even deformed nuclei to states near the neutron binding energyBn are calculated within the quasiparticle-phonon nuclear model. The wave functions of excited states include one- and two-phonon components. The calculations were made with the Pauli principle being or not included in the two-phonon components of the wave functions. It is shown that the radiativeE1- andM1-strength functions as well as the widths of giant dipole resonances in deformed nuclei are slightly influenced by the two-phonon components of the wave functions and they can be calculated in the RPA. ThekE1- andkM1-values are calculated for some deformed nuclei of the rare-earth and actinide region. The calculated values ofkE1 are 1.5–2 times larger and the values ofkM1 are somewhat less than the average values obtained in [14] from the analysis of available experimental data.

Influence of the superfluid pairing interaction on collective states in the finite-temperature random phase approximation

A set of finite-temperature RPA equations is obtained within the framework of the quasiparticle-phonon nuclear model using a separable multipole interaction. The calculations have been performed for the isovector dipole and isoscalar quadrupole modes in 58Ni. The author finds that the centroids of the giant resonances undergo a bending in the critical temperature region where the collapse of the pairing gap takes place.

Basic equations of the quasiparticle-phonon nuclear model for odd spherical nuclei

This paper obtains, in general form, the system of basic equations of the quasiparticle-phonon nuclear model for odd spherical nuclei. The equations take into account the anharmonicity of the vibrations of the even-even core and the corrections made necessary by the Pauli principle. It is shown that the system of equations contains all the variants of approximate equations of the quasiparticle-phonon model that are widely used in calculations.

System of equations of the quasiparticle-phonon nuclear model with allowance for phonon scattering at finite temperature

System of equations of the quasiparticle-phonon nuclear model with allowance for phonon scattering at finite temperature

Fragmentation of spin-dipole charge-exchange states in spherical nuclei

Fragmentation of spin-dipole charge-exchange states in spherical nuclei is studied within the quasiparticle-phonon nuclear model with the use of central residual forces. Calculations are performed for 90Zr, 120,124Sn, 124Te and 208Pb. It is shown that 10-25% of the transition strength is shifted from the region of the maximum towards large excitation energies; on the whole this region loses about 30%.

Transversal E1-Resonance in Spherical Nuclei

The spin-flip E1-states in medium and heavy spherical nuclei are investigated within the quasiparticle-phonon nuclear model. The RPA-calculations predict the existence of a collective 1--state formed by the isovector spin-dipole force. Its excitation energy is about 20 MeV. This state is intensively excited by the inelastic electron scattering at momentum transferred q ≈ 0.5-0.7 fm-1, at the scattering angles θ > 60° the main contribution to its excitation comes from the transversal form factor. Therefore, it can be recognized as the transversal E1-resonance. The interaction with two-phonon states causes a very strong spreading of the resonance, thus making its experimental observation hardly probable.

On vibrational states in deformed odd-A nuclei

The equations for the description of vibrational states in deformed odd-A nuclei are obtained within the quasiparticle-phonon nuclear model. In these equations the Pauli principle is taken into account in the quasiparticle plus phonon components of the wave functions. It is shown that if in these components the Pauli principle is not violated or is slightly violated, the corresponding vibrational states may exist in deformed odd-A nuclei. If the Pauli principle is strongly violated in the quasiparticle plus phonon state, its centroid energy is shifted towards higher energies, and it can be fragmented over several levels. The analysis of the available experimental data on the low-lying vibrational states in deformed odd-A nuclei has shown that the experimental data do not contradict the results of these calculations.

Inclusion of neutron-proton phonons in the quasiparticle-phonon nuclear model

Inclusion of neutron-proton phonons in the quasiparticle-phonon nuclear model

High-lying single-proton states in spherical nuclei

The fragmentation of high-lying single-proton states in 145Eu and 209Bi is calculated within the quasiparticle-phonon nuclear model. The results of the calculation are compared with the data for the proton stripping reactions 144 Sm(α, t) 145 Eu and 208 Pb(α, t) 209 Bi .

Nuclear properties in the lead region within the quasiparticle-phonon nuclear model

The properties of the low-lying states and giant resonances in 208Pb are calculated within the quasiparticle-phonon nuclear model, the model parameters being fixed. The fragmentation of the deep hole states 1 h 11 2 , 1 g 7 2 and 1 g 9 2 in 207Pb and 1 g 7 2 , 1 g 9 2 , 2 p 1 2 and 2 p 3 2 in 203, 205, 207Tl is calculated, and qualitative agreement with the available experimental data is obtained. The s-, p- and d-wave neutron strength functions are calculated for 206Pb + n and 207Pb + n resonances. Their energy dependence is correctly described up to 0.9 MeV above the neutron binding energy B n. The reduced E1 transition probabilities and the total photoabsorption cross sections σ γt in 206, 208Pb are calculated. It is shown that substructures observed in the energy dependence σ γt are caused by the fragmentation of one-phonon states. A fine structure of the isoscalar quadrupole resonance is explained, and the description of the LEOR and HEOR in 208Pb is obtained, which is in agreement with the experimental data.

Neutron-hole strength distributions in heavy nuclei: (II). The 144, 148, 152Sm( 3He, α) 143, 147, 151Sm and the 144, 148, 150, 152, 154Sm(p, d) 143, 147, 149, 151, 153Sm reactions

Valence and deep-lying neutron-hole strengths corresponding to orbits near and well below the Fermi surface have been observed in high-resolution studies of the 144, 148, 152Sm( 3He, α) and of the 144, 148, 150, 152, 154Sm(p, d) reactions at 70 and 42 MeV bombarding energy, respectively. The explored excitation energy range was 28 MeV for the ( 3He, α) experiment and about 12 MeV in the (p, d) study. Complete angular distributions have been measured in both cases and the data was analyzed within the framework of the distorted waves Born approximation theory of direct reactions. For the neutron closed shell target ( 144Sm), in addition to the well-known fragmentation of the 2d 5 2 and 1g 7 2 valence-hole strength, a new bump observed around 7.6 MeV excitation energy is excited in both reactions. This structure corresponds to the 1g 9 2 inner-hole strength in 143Sm and the analysis of the ( 3He, α) data suggests that more than 50% of the l = 4 strength can be found between 6 and 12 MeV. When one goes to the heavier Sm isotopes, the energy spacing between valence-hole states located above and just below the N = 82 shell decreases strongly and disappears in 151Sm as a result of increasing deformation. Combining good energy resolution and detailed analysis of the two reactions, rather complete spectroscopic information is obtained for the valence-hole strength distributions. With regard to inner-hole states, the energy spectra exhibit a narrow structure whose centroid energy decreases from 4.4 to 2.9 MeV when the mass number increases from A = 147 to A = 153. The main peak displays an asymmetric shape with an extremely large high-energy tail. The 1h 11 2 hole strength is split into the Nilsson Orbitals. The narrow bumps are found to carry a large fraction of the l = 5 and l = 2 hole strengths in 147,149,151,152Sm isotopes. In the high-energy tail of the structures one observes overlapping and increasing spreading of the g 7 2 , 2d 5 2 and possibly 1g 9 2 inner-hole strengths due to the disappearance of the N = 82 shell gap between N = 83 and N = 89 neutron numbers. The experimental hole strengths distributions are compared where possible to the predictions of the quasiparticle-phonon nuclear model or to the simple Nilsson model.

Radiative strength functions in odd- A spherical nuclei

The radiative strength functions for the partial γ-transitions from neutron resonances to the ground and low-lying states of odd- A spherical nuclei are calculated within the quasiparticle-phonon nuclear model. The fragmentation of one-quasiparticle and quasiparticle-plus-phonon states is calculated. This allowed one to calculate γ-transitions between the one-quasi-particle components (valence transitions) and γ-transitions between the quasiparticle-plus-phonon and one-quasiparticle components of the wave functions. The energy dependence of the strength functions C (E1, η) and C (M1, η) is calculated near the neutron binding energy B n for 55Fe and 59, 61Ni. The corresponding experimental data are described qualitatively. The contribution of the valence E1 transitions to the strength function is shown to be from 20% to 90%, and M1 transitions about 1%. The influence of the M1 giant resonance is important for M1 transition probabilities.

Magnetic dipole and quadrupole states of58Ni

The cross sections for the inelastic scattering of electrons with excitation of the 1+ and 2- states of 58Ni are calculated using the DWBA. Their structure is calculated within the quasiparticle-phonon nuclear model taking the interaction of one- and two-phonon states into account. The interaction is shown to be important for the explanation of the experimental data of Lindgren et al. (1976).

Fragmentation of two-quasiparticle states in spherical nuclei

Abstract The fragmentation of two-quasiparticle states in doubly even spherical nuclei is calculated witin the quasiparticle-phonon nuclear model. The fragmentation is due to the interactions leading to the formation of phonons and to the quasiparticle-phonon interaction. The spectroscopic factors for the “particle-valence particle” states in 92 Zr are calculated. The agreement with the experimental data of the reaction 91 Zr(d, p) 92 Zr is obtained. The centroid energy E jj0 and width Γ jj 0 are calculated for the configurations excited in the (p, d) reactions on odd- A isotopes of Cd, Sn and Te. It is shown that the valence particle-hole 1 g 9 2 configuration is localized and the excitation energies of 7–9 MeV. The corresponding experimental data are well described. The fragmentation of the states {1 g 7 2 , 1 g 9 2 −1 }, {3 s 1 2 , 1 g 9 2 −1 }, {2 d 3 2 , 1 g 9 2 −1 } and {1 h 11 2 , 1 g 9 2 −1 } in the Sn isotopes is calculated. Their strength is concentrated at the energies of 6.5–9.0 MeV. It is stated that the resonance-like structures observed in the (p, t) reaction on 112–124 Sn at the energy of 7–9 MeV are specified by the fragmentation of these states.

On collective two-phonon states in deformed nuclei

The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by 1–2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3–4 MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.

The effect of the Pauli principle on the fragmentation of one-quasiparticle states in spherical nuclei

The effect of the Pauli principle on the fragmentation of one-quasiparticle states in spherical nuclei is studied within the quasiparticle-phonon nuclear model. It is shown that the Pauli principle influences considerably the position and structure of a few low-lying states. The fragmentation of one-quasiparticle states at intermediate and high excitation energies is slightly affected by the Pauli principle, and the calculations can be performed by taking the Pauli principle into account roughly.

The description of the fragmentation of one-quasiparticle states in spherical nuclei

The fragmentation of hole states in spherical nuclei is calculated within the quasiparticlephonon nuclear model. The model equations and the numerical method for their solution are given. The influence of the “quasiparticle plus two phonon” components of the wave function and of phonons of different multipolarity on the fragmentation of one-quasiparticle states is investigated. The necessity of taking into account the “quasiparticle plus two phonon” components and of calculating with a large phonon basis is shown. The calculated values of the centroid E x , width Γ ↓ and spectroscopic factor S j , are in satisfactory agreement with the experimental data for the fragmentation of the neutron states 1 d 3 2 and 1f 7 2 in 57Ni, 1g 9 2 in Sn and 123Te, and of the proton state 1g 9 2 in 143Pm, etc. The calculated strength concentration of the lg 9 2 state decreases in the peak when passing from 115Sn to 119Sn. However, this decrease is less than that observed experimentally.

Effect of the Pauli principle on the excited states of doubly-even deformed nuclei

It is shown that the commutation relations between the quasiparticles forming phonons can correctly be taken into account within the quasiparticle-phonon nuclear model. The doubly-even deformed nuclei with the isoscalar and isovector multipole-multipole forces are studied. The exact and approximate secular equations are derived. It is shown that the two-phonon poles in the secular equation are shifted due to the Pauli principle. These shifts are large for the two identical collective phonons. In some cases pronounced shifts are found for the poles composed of a low-lying collective phonon and a collective phonon forming the giant resonance. In other cases the shifts are not large, as a rule.

Magnetic quadrupole resonance in spherical nuclei

The distribution of the M2 strength in spherical nuclei is studied within the quasiparticle-phonon nuclear model. It is shown that the interaction of the one- and two-phonon states affects strongly this distribution at the excitation energies E x > 15 MeV. In all the nuclei the strength of the M2 transitions is concentrated in the excitation energy region of 6–12 MeV. At these energies the calculated total value of B(M2)↑ is in good agreement with the experimental data in 90Zr and 208Pb. The calculations show that a group of states observed in 58Ni at an energy of about 7 MeV in the (e, e′) experiments is a part of the M2 resonance.

Description of the substructure in the radiative strength function of117Sn and119Sn

The total E1 and M1 photo-absorption cross section in 117Sn and 119Sn is calculated within the quasiparticle-phonon nuclear model. It is shown that at an energy of about 8 MeV the cross section has a substructure caused by the E1 transitions 3s1/2 to 2p1/2, 3s1/2 to 2p3/2 and a peak of the giant M1 resonance in the region of 8 MeV. Thus the authors have explained the substructure observed by Winhold et al. (1970).