Angular and energy dependence of (e,e′)(e,e^{\prime}) cross sections for orbital 1+^+ excitations

The main features of the $(e,e^{\prime})$ cross sections of low-lying orbital excitations with $K^{\pi} = 1^+$ in heavy deformed nuclei are studied in RPA on the example of $^{156}$Gd. The dependence of the DWBA E2 and M1 cross sections on the scattering angle $0^{\circ} < \theta < 180 ^{\circ}$ and incident electron energy $E_i < 210$ MeV is analyzed in PWBA. The cross section is larger for M1 than for E2 transitions at any angle if $E_i < 30$ MeV. The longitudinal (Coulomb) C2 excitation dominates the E2 response for $5^{\circ} < \theta < 170 ^{\circ}$. Only transverse M1 and E2 excitations compete for $\theta > 175 ^{\circ}$ and the former one is dominant for $q < 1.2$ fm$^{-1}$. The M1 response is almost purely orbital up to $q = 1.4$ fm$^{-1}$ even in backward scattering. Qualitative PWBA estimates based on the $q$-dependence of the form factors alone are not able to predict some important features of the $(e,e^{\prime})$ cross sections stemming from the strong magnetic and orbital character of the studied 1$^+$ excitations. The expectation for M1 over E2 dominance in backward scattering should not be extended to higher momentum transfers and incident energies.Comment: Latex, 28 pages, 12 postscript figures included using uufile

The Isovector Quadrupole-Quadrupole Interaction Used in Shell Model Calculations

An interaction $-\chi Q\cdot Q(1+B\vec{\tau}(1)\cdot \vec{\tau}(2))$ is used in a shell model calculation for $^{10}Be$. Whereas for $B=0$ the $2_1^+$ state is two-fold degenerate, introducing a negative $B$ causes an `isovector' $2^+$ state to come down to zero energy at $B=-0.67$ and an $S=1~L=1$ triplet ($J=0^+,~1^+,~2^+$) to come down to zero energy at $B=-0.73$. These are undesirable properties, but a large negative $B$ is apparently needed to fit the energy of the isovector giant quadrupole resonance.Comment: 12 pages, revtex, 2 figures (available on request

Competing electric and magnetic excitations in backward electron scattering from heavy deformed nuclei

Important $E2$ contributions to the $(e,e^{\prime})$ cross sections of low-lying orbital $M1$ excitations are found in heavy deformed nuclei, arising from the small energy separation between the two excitations with $I^{\pi}K = 2^+1$ and 1$^+1$, respectively. They are studied microscopically in QRPA using DWBA. The accompanying $E2$ response is negligible at small momentum transfer $q$ but contributes substantially to the cross sections measured at $\theta = 165 ^{\circ}$ for $0.6 < q_{\rm eff} < 0.9$ fm$^{-1}$ ($40 \le E_i \le 70$ MeV) and leads to a very good agreement with experiment. The electric response is of longitudinal $C2$ type for $\theta \le 175 ^{\circ}$ but becomes almost purely transverse $E2$ for larger backward angles. The transverse $E2$ response remains comparable with the $M1$ response for $q_{\rm eff} > 1.2$ fm$^{-1}$ ($E_i > 100$ MeV) and even dominant for $E_i > 200$ MeV. This happens even at large backward angles $\theta > 175 ^{\circ}$, where the $M1$ dominance is limited to the lower $q$ region.Comment: RevTeX, 19 pages, 8 figures included Accepted for publication in Phys Rev

High-energy scissors mode

All the orbital M1 excitations, at both low and high energies, obtained from a rotationally invariant QRPA, represent the fragmented scissors mode. The high-energy M1 strength is almost purely orbital and resides in the region of the isovector giant quadrupole resonance. In heavy deformed nuclei the high-energy scissors mode is strongly fragmented between 17 and 25 MeV (with uncertainties arising from the poor knowledge of the isovector potential). The coherent scissors motion is hindered by the fragmentation and $B(M1) < 0.25 \; \mu^2_N$ for single transitions in this region. The $(e,e^{\prime})$ cross sections for excitations above 17 MeV are one order of magnitude larger for E2 than for M1 excitations even at backward angles.Comment: 20 pages in RevTEX, 5 figures (uuencoded,put with 'figures') accepted for publication in Phys.Rev.

The effects of deformation and pairing correlations on nuclear charge form factor

A set of moderately deformed $s-d$ shell nuclei is employed for testing the reliability of the nuclear ground state wave functions which are obtained in the context of a BCS approach and offer a simultaneous consideration of deformation and pairing correlations effects. In this method, the mean field is assumed to be an axially symmetric Woods-Saxon potential and the effective two-body interaction is a monopole pairing force. As quantities of main interest we have chosen the nuclear form factors, the occupancies of the active (surface) orbits and the Fermi sea depletion, which provide quite good tests for microscopic descriptions of nuclei within many body theories. For our comparisons with results emerging from other similar methods, an axially deformed harmonic oscillator field is also utilized.Comment: 20 pages, 12 figures, 2 table

Parity-Dependence in the Nuclear Level Density

Astrophysical reaction rates are sensitive to the parity distribution at low excitation energies. We combine a formula for the energy-dependent parity distribution with a microscopic-macroscopic nuclear level density. This approach describes well the transition from low excitation energies, where a single parity dominates, to high excitations where the two densities are equal.Comment: 4 pages, 3 figures; contribution to Nuclei In The Cosmos VIII, to appear in Nucl. Phys.

Influence of atmospheric circulation on the spatial distribution of precipitation in the area of Sofia city

The study aims to reveal spatial distribution of precipitation in the area of Sofia city during the decade 2013 - 2022 and the influence of atmospheric circulation. Statistical methods and cartographic approach are the main tools in this research. The spatial distribution of precipitation is characterized by low amounts (560 mm) in the northern and northeastern parts of Sofia depression and high amounts (760 mm) in the southern part. The main factor for this spatial distribution of precipitation is atmospheric circulation. The relief has a significant modifying effect and affects precipitation through several mechanisms. The most important is the location of mountain slope relative to the main direction of transport of air masses. Leeward slopes receive less precipitation and windward slopes receive more. The second mechanism of influence is anthropogenic relief (high buildings), which is a positive relief form compared to the surrounding plane having respective windward and leeward slopes. This study revealed a third mechanism of relief influence on spatial distribution of precipitation. The large difference in the height of the mountains located south of Sofia creates a significant difference in the air temperature in Sofia depression during a transport of air masses from south and southwest. This is due to the stronger foehn effect of the higher mountain (Vitosha) compared to the foehn effect of the lower mountains (Lyulin, Lozenska Planina), which creates a tongue of higher air temperature northeast of Vitosha, which reaches the southern and southwestern slopes of Stara Planina. The higher temperatures in this tongue create stronger upward air movements, which in turn increase the amount of precipitation. Secondary, but still important factors that affect the spatial distribution of precipitation in Sofia region are the urban heat island and the increased content of aerosols in the air in and over the city

Orbital and Spin Magnetic Dipole Strength in a shell model calculation with ΔN\Delta N=22 excitations: ^8\mbox{Be}

The magnetic dipole strength and energy-weighted strength distribution is calculated in ^8\mbox{Be}, as well as the separate orbit and spin parts. All $\Delta N$=$2$ excitations over and above (and including) the configuration $0s^4$$0p^4$ are included. The interaction has a central, two-body spin-orbit and a tensor part. The energy- independent and energy-weighted {\underline orbital} strength distribution is remarkably insensitive to the presence or absence of the spin-orbit or tensor interaction -not so the spin strength. The energy-weighted strength distribution can be divided into a low enegy and a high energy part. The high energy orbital part is somewhat less but close to the low energy part, in fair agreement with a prediction that they be equal by de Guerra and Zamick and by Nojarov. There is a wide plateau separating the low energy part from the high energy part.Comment: 12 pages (4 figs/on request) \#RU944

Self-Consistent Velocity Dependent Effective Interactions

The theory of self-consistent effective interactions in nuclei is extended for a system with a velocity dependent mean potential. By means of the field coupling method, we present a general prescription to derive effective interactions which are consistent with the mean potential. For a deformed system with the conventional pairing field, the velocity dependent effective interactions are derived as the multipole pairing interactions in doubly-stretched coordinates. They are applied to the microscopic analysis of the giant dipole resonances (GDR's) of ${}^{148,154}Sm$, the first excited $2^+$ states of Sn isotopes and the first excited $3^-$ states of Mo isotopes. It is clarified that the interactions play crucial roles in describing the splitting and structure of GDR peaks, in restoring the energy weighted sum rule, and in reducing the values of $B(E\lambda)$.Comment: 35 pages, RevTeX, 7 figures (available upon request), to appear in Phys.Rev.