2p-2h States Research Articles

Microscopic nuclear dissipation: (II). Damping of collective states in subspaces which include 2p-2h states

We have formulated a microscopic, nonperturbative, time reversible model which exhibits a dissipative decay of collective motion for times short compared to the system's Poincaré time. The model assumes an RPA approximate description of the initial collective state within a restricted subspace, then traces its time evolution when an additional subspace is coupled to the restricted subspace by certain simplified matrix elements. It invokes no statistical assumptions. The damping of the collective motion occurs via real tansitions from the collective state to other more complicated nuclear states of the same energy. It corresponds therefore to the so called “one-body” long mean free path limit of nuclear dissipation when the collective state describes a surface vibration. When the simplest RPA approximation is used, this process associates the dissipation with the escape width for direct particle emission to the continuum. When the more detailed second RPA is used, it associates the dissipation with the spreading width for transitions to the 2p-2h components of the nuclear compound states as well. The energy loss rate for sharp n-phonon initial states is proportional to the total collective energy, unlike the dissipation of a classical damped oscillator, where it is proportional to the kinetic energy only. However, for coherent, multi-phonon wave packets, which explicitly describe the time-dependent oscillations of the mean field, dissipation proportional only to the kinetic energy is obtained. Canonical coordinates for the collective degree of freedom are explicitly introduced and a nonlinear frictional hamiltonian to describe such systems is specified by the requirement that it yield the same time dependence for the collective motion as the microscopic model. Thus, for the first time a descriptive nonlinear hamiltonian is derived explicitly from the underlying microscopic model of a nuclear system.

Gamow-teller states in 208Pb

We investigate coherent spin-isospin excitations of nucleons and isobars in 208Pb in the long-wavelength limit (spin-isospin zero sound). Both NN− and ΔN− particle-hole channels are considered within a coupled RPA calculation using a Landau-Migdal type ph residual interaction. We obtain energy and strength of the giant isobaric Gamow-Teller (GT) state and discuss its influence on the nucleonic GT excitation. The coupling of this mode to 2p-2h states is also discussed. We emphasize the role of surface vibrational modes as dominant decay channels.

Relations among the quenching strengths of magnetic transitions due to theΔisobar excitation inN≠Znuclei

A possible excitation scheme of particle-hole states in Nnot =Z nuclei is worked out within the isospin formalism. Particle-hole states with a definite isospin are decomposed into 1p-1h (particle-hole), 2p-2h, and 3p-3h states. This decomposition enables us to relate transition strengths from the ground state to the excited states and those in the adjacent nuclei. The same thing is done for ..delta.. isobar-hole states. Using these results, we obtain the relations among the quenching strengths of magnetic transitions in Nnot =Z nuclei. In particular, we apply these relations to the M1 states around /sup 48/Ca and /sup 90/Zr and compare the results with experimental data obtained by (p,n), (p,p'), and (e,e') experiments on /sup 48/Ca and /sup 90/Zr.

Nuclear dynamics and quasi-elastic electron scattering

We present results of calculations of the longitudinal and transverse response function for inelastic electron scattering from $^{56}\mathrm{Fe}$ and $^{12}\mathrm{C}$. In the impulse approximation it is found that the calculated longitudinal response is approximately forty percent too large for $^{56}\mathrm{Fe}$. We discuss those aspects of nuclear dynamics which could account for this discrepancy and suggest that the depletion of the shell model orbitals through various (short-range) correlation effects may play an important role. It is suggested that a significant longitudinal response may exist at energies above the quasi-elastic domain; this response would involve the excitation of 2p-2h states. In our model there is a significant disagreement between theory and experiment for the transverse response. We ascribe this disagreement to meson-exchange-current effects; however, we present no calculations of such effects in this work. Quantitative studies of these effects in finite nuclei are required. If our model for the quenching of the longitudinal response in the quasi-elastic domain proves to be correct, we can infer that quasi-elastic electron scattering studies may provide a measurement of the average probability of the occupation of a shell model orbital.

Quenching of the electromagneticM1strength due to the first order mesonic and ground state correlation effects

The effects of the 2p-2h ground state correlation, isobar-hole excitation, pion pair current, and pionic current on the electromagnetic $M1$ strength are calculated as a first order perturbation correction, for $^{12}\mathrm{C}$, $^{48}\mathrm{Ca}$, $^{90}\mathrm{Z}$, and $^{208}\mathrm{Pb}$ using Hartree-Fock wave functions. The isobar-hole contribution is the dominant quenching mechanism in heavier nuclei, though the enhancement effect of the pion pair current is not at all negligible. We also comment on the Gamow-Teller strength.NUCLEAR STRUCTURE Calculated $M1$ strength $^{12}\mathrm{C}$, $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, $^{208}\mathrm{Pb}$ including ground state correlation, isobar-hole excitation, meson exchange currents.

Nuclear dissipation as damping of collective motion in the time-dependent RPA: (I). The microscopic model

A microscopic model for describing nuclear dissipation as the damping of collective motion in the time-dependent RPA is considered. The collective state is defined as a solution of the RPA equations of motion in a restricted subspace, S 1, of discrete 1p-1h states. The damping of the collective motion is described by the time evolution of the wave packet which solves the time-dependent Schrödinger equation in an extended subspace, S, when initialized with the collective state. In the present paper we consider additional state of the 1p-1h structure only. The RPA solution for the wave packet describing the damping enables one to calculate — as a function of time — both the probability amplitude for finding the system in the collective state and the collective energy, and to extract their time decay under appropriate conditions. The rate of decrease of the collective energy is interpreted as the energy dissipation rate.

Configurations of particle-hole states in 16O

The analysing powers of the 17O( 3 He,α) 16O reaction populating twelve 1p-1h states up to 20.5 MeV excitation energy were measured to determine the distribution of the j π= 3 2 − and 1 2 − f transfer strengths. The results indica that, with one exception, the states observed have practically pure ( 1 d 5 2 1 p −1 1 2 ) or ( 1 d 5 2 1 p −1 3 2 ) configurations, in agreement with shell-model calculations.

Dynamics of single-particle and collective excitations in heavy nuclei

The propagation of single-particle and small-amplitude collective excitations in a heavy nucleus is considered. We calculate perturbatively corrections to the mean-field approximation induced by the coupling of one-particle and collective motion via the residual particle-hole interaction. Special attention is paid to the energy variation of the quasiparticle effective mass near Fermi energy. We conclude from the calculation that particles and holes excited in low multipolarity giant resonances have average effective masses of the order of 0.8 m rather than m. The mechanism for the decrease is provided by the enforced decoupling of the quasiparticles from surface oscillations due to the high frequency of the giant resonances. We also study the role of surface modes in the decay of giant resonances. Considerable reduction of the damping into 2p-2h states expected from the absorptive part of the optical potential is found. The correlated particle-hole pairs interact with each other by exchanging surface oscillations which adds a destructive interference term to the decay widths of giant resonances. The reduction depends on the multipolarity of the mode and is only large for low angular momenta.

Role of 2p-2h states in weak 0 +−0 − transitions in A = 16 nuclei

Muon-capture and β-decay rates for the transitions 16O(0 +, ground) (a3) 16N(0 −, 120 keV) are calculated to second order in perturbation theory. With a one-boson-exchange residual interaction, reasonable agreement to the decay rates Λ μ and Λ β can be achieved, but only if meson-exchange corrections are incorporated in the transition operator. These corrections strongly influence the time-like part of the axial-vector current.

The isospin splitting of isovector monopole excitations

The excitation energy of the isovector monopole state is calculated for a series of nuclei with N > Z using a simple residual particle-hole interaction and a basis of wave functions which conserve isospin. Such wave functions include 2p2h configurations in addition to 1p1h states. The splitting between the T 0 + 1 and T 0 components of the isovector monopole state is obtained. Using the wave function of the T 0 + 1 component the amount of isospin mixing in the ground states is estimated.

Fourth-order high-lying contributions to the ground-state energies of some closed-shell nuclei

We discuss a complete fourth-order calculation, in an oscillator basis, of the ground-state energies of closed-shell nuclei using graphical techniques. The calculations, carried out by evaluating all linked Goldstone graphs that contribute in the subspace of intermediate excitations up to 4 ω for 4He and 16O show that the linked fourth order 3p-3h and 4p-4h intermediate state graphs are small compared to the corresponding 1p-1h and 2p-2h intermediate state Goldstone graphs. Both the original and the saturating Sussex matrix elements are used and the effect on the order-by-order convergence of modifying the unperturbed single-particle energies is studied. The sum of linked graphs is extrapolated from the lowest orders in the interaction using Padé approximants, and encouraging results are obtained.

Convergence studies for the one-body mass radius operator of some closed-shell nuclei

The convergence properties of the perturbation series for the mass radius operator are studied in detail using a harmonic oscillator basis. The systems considered are the ground states of the closed shell nuclei 4He, 16O and 40Ca. Calculations are carried out to third order in the nuclear interaction and include up to 4ħω excitations for 4He and 16O, and up to 2ħω excitations for 40Ca. Goldstone graph components are used for graphs with at most 2p-2h intermediate states and Goldstone graphs for graphs with 3p-3h intermediate states. Both, the original and the saturating Sussex matrix elements (SME) are used. Some diagonalizations and inversions are also considered. The mass radius operator results with the original SME give large negative contributions that result in small rms radii. The results with the saturating SME indicate a slow order by order convergence at the value of the size parameter b that gives saturation in the first order energy. However, in this case, the individual perturbation orders and the total corrections, for the mass radius operator, are small for each of the above three nuclei at these values of b, and reasonably good agreement with experimental rms radii is obtained.

Calculation of widths of giant monopole resonances in 16O and 40Ca

Self-consistent RPA calculations based on the Skyrme interaction are carried out for isoscalar and isovector monopole resonances in 16O and 40Ca. The usual RPA is improved by taking account of couplings to the continuum as well as 2p-2h states as a form of the self-energy of particle-hole states. The linear response functions are calculated as a function of the energy. Two types of parameter sets III and IV for the Skyrme interaction are found to give rather different results. The validity of our approximations is discussed.

T=0 pairing vibrations in16O

In the reaction 14N(3He,p)16O at 15 MeV bombarding energy, the observed excitation energies, L values and cross sections for 16O levels at 14927+or-2 and 15785+or-5 keV establish them as 2p-2h states with Tp=Th=0, and strongly suggest Jpi =1+ and 3+ respectively.

Pre-equilibrium particle decay in the photonuclear reactions

Calculations of particle energy spectra resulting from the photonuclear reactions at energies below the meson production threshold have been carried out in the framework of combining the pre-equilibrium exciton model and the quasideuteron model. A 2p-2h initial state in the exciton model is assumed because the quasideuteron absorption is the dominant process in the energy region above giant resonance. With this combined model the subsequent secondary interactions of the emerging particle with the rest of the nucleus following the initial photon-nucleus interaction are appropriately taken into account. The experimental difference energy spectra of fast photoneutrons from several elements (Al, Cu, In, Sn, Ta, Pb, Bi, and U) at bremsstrahlung energies of 55 and 85 MeV were compared with the theoretical predictions. General agreements in both spectral shapes and cross sections are obtained. The relative yields of the reactions ($\ensuremath{\gamma},xn$) resulting from monoenergetic photons on $^{127}\mathrm{I}$ at 50, 100, and 150 MeV are also predicted reasonably well by the combined model together with the conventional evaporation theory.NUCLEAR REACTIONS $^{27}\mathrm{Al}(\ensuremath{\gamma},x)$, $^{63}\mathrm{Cu}(\ensuremath{\gamma},x)$, $^{115}\mathrm{In}(\ensuremath{\gamma},x)$, $^{118}\mathrm{Sn}(\ensuremath{\gamma},x)$, $^{181}\mathrm{Ta}(\ensuremath{\gamma},x)$, $^{207}\mathrm{Pb}(\ensuremath{\gamma},x)$, $^{209}\mathrm{Bi}(\ensuremath{\gamma},x)$, $^{235}\mathrm{U}(\ensuremath{\gamma},x)$, ${E}_{\ensuremath{\gamma}}=55 \mathrm{and} 85$ MeV bremsstrahlung. $^{12}\mathrm{C}(\ensuremath{\gamma},x)$, ${E}_{\ensuremath{\gamma}}=110$ MeV bremsstrahlung. $^{127}\mathrm{I}(\ensuremath{\gamma},xn)$, ${E}_{\ensuremath{\gamma}}=50, 100, \mathrm{and} 150$ MeV. Pre-equilibrium exciton, quasideuteron, and statistical compound nucleus models analyses.

Spectroscopy of 16C

The 14C(t, p) 16C reaction locates five new states in 16C, at excitation energies of 3120 ± 15, 3983 ± 10, 4136 ± 10 and 6109 ± 15 keV, in addition to the g.s. and 1.76 MeV states. The 3.02 and 3.98 MeV states appear to be the second 0 + and 2 + 2p-2h states, respectively. The 4.14 MeV state has J π = 4 + and the 6.11 MeV state has J π = 2 +, 3 −, or 4 +.

Giant Monopole State in the Double-Closed Shell Nucleus with Excess Neutrons

approximation with good isospin basis. All 1p-1h excitation states of 2hw jump are taken in our configuration. The coupling constants of isoscalar and isovector monopole-monopole interactions are determined by the self-consistent field method. Our results show fine agree­ ment with experimental data obtained by electron and nucleon inelastic scatterings. The effects of monopole core polarization on isospin mixing and isotope shift are also discussed.

Study of the ground-state correlations and continuum model calculations for photonuclear reactions

Using the effective operator formalism, the importance of ground-state correlations on photonuclear cross sections is studied. For purposes of orientation, a bound-state calculation is first performed to take into account the mixing of 2p-2h and 3p-3h configurations into the 1p-1h dipole states. Inclusion of these configurations is found to affect the energies of the 1p-1h states in opposite directions and the combined effect, including that on the transition strengths, is negligible. Most of the reduction in the absorption comes from the ground-state correlations of which the A -dependence is examined with a model interaction. We then proceed to calculate the excitation function for the reactions using effective dipole matrix elements obtained from the continuum wave functions of the coupled-channels calculation. Application to the case of 16 O leads to a reduction of about 25 % in the cross sections.

Neutron correlations in the 41K ground state and T = 1 2p-2h states in 40K

Differential cross sections have been measured for 41(d, t) 40K and 41K(p, d) 40K at 15 MeV using a magnetic spectrograph with electronic detection by proportional-counter-scintillator telescopes or semiconductor detectors. Knowledge of the structure of the 40K multiplets ( ν f 7 2 , π d 3 2 −1 ) and ( ν p 3 2 , π d 3 2 −1 ) permits the determination of amplitudes and relative phases for various configurations and neutron correlations in the 41K ground state. Spectroscopic factors for neutron pick-up to states in 40K are strongly influenced by the interference of transition amplitudes. In the (d, t) reaction T= 1, 2p-2h states are also observed.

The damping of the giant resonances in heavy and medium-heavy nuclei

Abstract The damping of the giant resonances in heavy and medium-heavy nuclei can be described by thermalization and cooling-off processes. The direct emission of particles, which is strongly inhibited by Coulomb and centrifugal barriers is neglected here. In the damping process, which begins with the thermalization, the 1p-1h giant resonance states induced by the incoming electromagnetic field are scattered inelastically due to the presence of two-body residual forces into other 1p-1h and 2p-2h states. In heavy nuclei there exist, at the energy of the giant resonance, several hundreds of such 2p-2h states. The 1p-1h dipole and quadrupole basis states for the diagonalization of the Hamiltonian are obtained from a spherical Nilsson potential. The density of the 2p-2h states obtained from the same potential are then used to determine the energy dependence of the widths of the giant resonances.