Second Coulomb energy differences of isospin triplets in the 2s-1d shell

Second Coulomb energy differences, which in the present case are proportional to the tensor Coulomb energy, are calculated for 0⁺, T = 1 ground states in the region 18 ≦ A ≦ 42 using a shell model that includes a pairing interaction. The calculation is done with a mathematical formalism that includes p-n pairs as well as p-p and n-n pairs. Besides an enhancement of proton-pair Coulomb energies, the pairing interaction is responsible for lowering the Coulomb energy of N = Z members of isospin triplets and also gives rise to an important term in the second energy difference. Using pairing strengths derived from fitting energy levels for mass-18 and mass-42 nuclei, results of the calculation reproduce experimental second energy differences extremely well.     

Separable interactions and liquid 3He

A rigorous expression is given for the free energy of a system of fermions in the presence of a magnetic field interacting via a pairing hamiltonian in the weak-coupling limit. Starting from this expression Landau expansions are derived in two special cases, i.e. the case of general l-wave pairing in zero field and the case of l = 1 pairing, which applies to liquid ³He, in non-zero field.     

Fusion and transfer cross sections of 3He induced reaction on Pt and Au in energy range 10–24.5 MeV

In experiments performed by accelerated ion ³He-beam irradiated gold and platinum targets on the cyclotron U-120M of the Nuclear Physics Institute of the Czech Academy of Sciences, ?e?, reactions of complete and incomplete fusion and nucleon transfer reactions in the ³He energy range from 10 to 24.5 MeV have been investigated. To determine the yield of the nuclides resulting from the nuclear reaction, the activation technique has been used. The obtained data are analyzed using models based on statistical calculations and compared with similar results for other light stable particles. Transfer reactions with positive Q values have relatively high cross sections in the energy range below the Coulomb barrier. These cross sections continue to grow with increasing ³He energy, and, in the case of capturing neutron from target nucleus by a nucleus of ³He, the excitation functions of these reactions reach their maximum almost at the Coulomb barrier of the reactions.     

Binding energies of even-even superheavy nuclei in a semi-microscopic approach

The structure of some even-even superheavy nuclei with the proton number Z = 98?120 is studied using a semi-microscopic but not self-consistent model. The macroscopic energy part is obtained from the Skyrme nucleon-nucleon interaction in the semi-classical extended Thomas-Fermi approach. A simple but accurate method is derived for calculating the direct part of the Coulomb energy. The microscopic shell plus pairing energy corrections are calculated from the traditional Strutinsky method. Within this semi-microscopic approach, the total energy curves with the quadrupole deformation of the studied superheavy nuclei were calculated. The same approach features the well known ²⁰⁸Pb or ²³⁸U nuclei. For each nucleus the model predictions for the binding energy, the deformation parameters, the half-density radii and comparison with other theoretical models are made. The calculated binding energies are in good agreement with the available experimental data.     

Stark interaction in then s n p z 3 P 1 levels of zinc and cadmium

The tensor polarizabilities of then s n p z ³ P ₁ levels of Zn and Cd were measured using optical double resonance. From the rf-resonance signals in parallel electric and magnetic fields, the following tensor polarizabilities were deduced: Zn,α _ten(4s4pz ³ P ₁)=1.83(8) kHz/(kV/cm)²; Cd,α _ten(5s5pz ³ P ₁)=1.77(8) kHz/(kV/cm)². Theoretical values were calculated using Coulomb approximation. The results were then compared with previous theoretical and experimental values and, in addition, with values for Hg. Theoretical results obtained by a modified Sternheimer method (E.J. Robinson: J. Opt. Soc. Am.59, 782 (1969)) are in better agreement with the experimental values than the results of the Coulomb approximation calculations.     

Coulomb contributions to nuclear radii and energies

The effect of including the isospin non-scalar Coulomb interaction (also taking into account the finite proton size) in binding energy and rms radius calculations for the closed shell nuclei ⁴He, ¹⁶O and ⁴⁰Ca is discussed in detail. Using the saturating Sussex matrix elements and including 0 + 2?ω excitations it is found that the major Coulomb contribution is in the first order, and that the pure second-order Coulomb contribution to the energy, near the saturation value of the size parameter for each nucleus, is more important than the mixed second-order contribution. Finally, for third order and above one can safely neglect the pure Coulomb contributions compared to the mixed ones which are in turn small compared to the pure nuclear contribution, in that order.     

Study of form factors for single-proton transfer reactions on152Sm,154Gd and156Gd

The (³He,d) and (α,t) single-proton transfer reactions on targets of¹⁵²Sm,¹⁵⁴Gd and¹⁵⁶Gd were studied at 35MeV incident energy. Differential cross sections of rotational states built upon various single-proton configurations are compared with results of DWBA calculations which employed various radial form factors. The agreement between calculated and measured reaction cross sections is found to improve significantly when the commonly used spherical bound-state potentials are replaced by deformed ones, including deformed Coulomb and spin-orbit wells, and projected form factors are used to calculate DWBA cross sections. Discrepancies in the differential cross sections so large that they cannot be attributed to band mixing phenomena are readily explained by form factor effects.     

Elastic scattering of 3He and 4He at incident energies near the coulomb barrier

The elastic scattering of ³He and ⁴He from Zr, Mo, Cd, and Te isotopes is studied at incident energies near the Coulomb barrier. Marked differences are observed between the excitation curves of ³He and ⁴He. These differences are shown to be due to a large surface absorption in the ³He scattering. A systematic study of the size parameters deduced from the present and other ⁴He experiments shows deviations from the $\text{A}\text{1}\text{3}$ law for nuclei near closed neutron shells.     

Neutron star matter superfluidity and superconductivity

The possibility of superfluidity or superconductivity in neutron or proton subsystems in the nuclear-matter region in neutron stars is investigated. The energy gap and corresponding critical temperature and critical magnetic field is calculated or estimated as function of density or Fermi momentum. In the calculations are used reaction matrix elements calculated earlier by means of Brueckner theory by the author. The final results indicate that neutron superfluidity, corresponding specifically toS-state pairing, may exist in a low-density shell in the nuclear-matter region of a neutron star. There is probably anisotropic neutron superfluidity, corresponding to the³ P ₂ or the singletD state, for higher densities. Superfluidity or superconductivity, corresponding toS-state pairing for the proton subsystem, is quite likely in most of the nuclear-matter region. The expected temperatures and magnetic fields in neutron stars seem to be well below the estimated critical temperatures or critical magnetic fields corresponding to the calculated values of the energy gap. However, similar methods have earlier predicted a much too high critical temperature for liquid³He.     

Analysis of excitation functions from light ion induced reactions in the EXCLUSIVE INDEX model

The previously introduced EXCLUSIVE INDEX model allows to predict the population of 6 residual nuclei including the primary compound nucleus through two stages of the preequilibrium phase. The present version is limited to maximum two-nucleon emission. The preequilibrium ejectiles may reduce the brought-in rotational energy by a model of maximum angular momentum decoupling. Subsequent evaporation of protons, neutrons andα-particles is treated in the frame of the Weisskopf-Ewing ands-wave approximation considering pairing effects only in compound nucleus state densities. The sensitivity of essential preequilibrium parameters on the shape of calculated excitation functions is tested. The model predictions well compare to excitation functions fromp, d,³He and⁴He induced reactions including the large set from the reaction⁹³Nb(⁴He,xn yp) up to 170 MeV bombarding energy. The general importance of two-nucleon preequilibrium emission is accentuated in several examples. The deduced preequilibrium parameters corroborate the results from the INDEX model analysis of nucleon spectra.     

Low-energy fusion cross sections of D + D and D + 3He reactions

The D(d, n)³He and D(d, p)T reactions have been investigated at E_c.m = 2.98 to 162.5 keV and the ³He(d, p)⁴He reaction at E_c.m. = 6.95 to 141.8 keV. The studies involved high-current accelerators with well-known beam characteristics and windowless gas target systems of the extended and quasi-point supersonic jet type. The measurement of absolute cross sections, angular distributions and excitation functions is reported. The data extend into the thermal energy region of future fusion reactors. The results for the D(d, n)³He and D(d, p)T reactions are in good agreement with previous work, while substantial differences are found for ³He(d, p)⁴He.     

In-beam spectroscopy of231Pa

Information on energy levels and onE 2 andM 1 matrix elements in²³¹Pa has been obtained using conversion-electron and gamma-ray spectroscopy following the²³²Th(p, 2n)²³¹Pa reaction and Coulomb excitation of the radioactive target²³¹Pa by⁴He and³²S ions. The results are analyzed in the framework of the rotational model, applied to the rotational band built on the 1/2^?[530] Nilsson state whose 3/2^? member forms the ground state of this nucleus. The deviations of the level energies from the rigid-rotor values can be described by Coriolis couplings. The analysis of the Coulomb-excitation process shows that a constant set of rotational parameters Q₀, g_R, g_K, andb can fairly well account for the measured line intensities.     

Absence of proton weak coupling states in93Nb

The reactions⁹³Nb(p, p)⁹³Nb,⁹³Nb(p, n)⁹³Mo, and⁹³Nb(p, p′) through isobaric analog resonances in⁹⁴Mo have been used to study the structure of low-lying⁹³Nb states, specifically the degree to which these states can be described as single protons coupled to the core states of⁹²Zr. Excitation curves were obtained from 5.8 to 7.6 MeV incident proton energy, for eight states in⁹³Nb. Results of this work are compared to results from Coulomb excitation studies,⁹³Nb(n, n′γ),⁹³Nb(d,p),⁹²Zr(³He,d),⁹⁴Mo(d,³He) and other related work.     

Cross sections of 43Sc, 44Sc, 46Sc isotopes formed in the 45Sc + 3He reaction

Reactions ⁴⁵Sc(³He, αn)⁴³Sc, ⁴⁵Sc(³He, α)⁴⁴Sc and ⁴⁵Sc(³He, 2p)⁴⁶Sc in the ³He energy range of 5 to 24 MeV are investigated in experiments performed with a ³He ion beam during the irradiation of U-120M cyclotron scandium targets. Activation is used to determine the yield of nascent Sc isotopes. The γ activity induced in targets is measured using a high-resolution HPGe detector. The character of the excitation function changes during the formation of these ions and differs from the excitation functions for deuterons, despite the low bond energy of ³He and the positive values of the Q reactions leading to the formation of ⁴⁴Sc and ⁴⁶Sc isotopes. The cross sections of ⁴⁴Sc formation reach their maximum value at the Coulomb barrier of the reaction, due to the stable ⁴He nucleus that accompanies the formation of ⁴⁴Sc. The contribution from different reaction mechanisms to the cross sections of ⁴³Sc, ⁴⁴Sc, and ⁴⁶Sc isotope formation are considered.     

Preliminary results of the study of the d(d,n)3He reaction in the astrophysical energy range with the use of a Hall plasma accelerator

The possibility of using a plasma accelerator based on a pulsed Hall ion source to study the characteristics of pd, dd, d³He, ³He, and⁴He reactions in the astrophysical energy range (2–12 keV) has been considered. The preliminary experimental data on measurement of the astrophysical S factor for the dd reaction (dd → ³He + n (2.5 MeV)) at average deuteron collision energies E _col = 4.5 and 4.95 keV and the deuteron beam energy spread FWHM = 18% are reported. The found value of the S factor is in agreement with the results of the experiments carried out by us previously using linear plasma in the inverse Z-pinch configuration.     

The beta-decay of 8He

A many-level, many-channel R-matrix formula is used to fit the measured ⁸He β-decay data, including the half-life, branching ratios and delayed neutron and triton energy spectra. Satisfactory fits are found with contributions from four 1⁺ levels of ⁸Li, at 0.98, 3.08, 5.15 and 9.06 MeV. The 32 reduced width amplitudes are taken from a shell-model calculation, with only two requiring adjustment. Gamow-Teller matrix elements obtained from the fits are in reasonable agreement with shell-model values.     

Quadrupole collective properties of 114Cd

The nucleus ¹¹⁴Cd has been Coulomb excited using beams of ¹⁶O, ⁴⁰Ca, ⁵⁸Ni and ²⁰⁸Pb. Several new states have been observed and an almost complete set of reduced E2 matrix elements for the lowest-lying positive-parity states in ¹¹⁴Cd have been measured. In total, about 40 E2 matrix elements have been determined in a model-independent way, including the static quadrupole moments of the 4⁺₁, 6⁺₁, 2⁺₂ and 2⁺₃ states. Large negative static quadrupole moments were found for the 4⁺₁ and 6⁺₁ states and a large positive quadrupole moment for the 2⁺₂ state. All E2 matrix elements involved in the deexcitation of the quintuplet of states at an energy of about 1.2 Me V were determined. The data are compared with predictions by various models, including a configuration mixing calculation within the framework of the IBA model, the harmonic vibrator and a model in which the states of a near-harmonic vibrator are mixed with those of a rotational intruder band with a large deformation. Although no perfect match is obtained, the data favour a vibration-like structure involving levels up to the four-quadrupole phonon multiplet.     

Analyzing power of n-3He elastic scattering from 1 to 2 MeV

Measurements of the analyzing power A_y of the elastic n-³He scattering in the energy range from 0.95 to 2.0 MeV are reported. These results improve considerably the precision of the data base in the low energy domain. Recent R-matrix predictions are used as starting parameters in phase-shift analyses. The comparison with p-³H and p-³He data at nearby energies reveals the importance of Coulomb effects at these low energies and of the isospin structure of the A = 4 system.     

Hartree-Fock and Hartree-Bogolyubov calculations inp shell nuclei

Hartree-Fock (HF) and Hartree-Fock-Bogolyubov (HFB) calculations have been performed for the 1p shell nuclei. Nuclear deformations are assumed to be at most axially symmetric. The HFB transformation is restricted to allow forp-p andn-n pairing only.Volkov's force, a soft-core, two-body interaction of semi-realistic nature, is used which does not produce any single-particle spin-orbit splittings. Coulomb force and the usual correction for centre-of-mass motion are taken into account. The calculations are carried out in a single-particle basis including all states up to principle oscillator quantum numberN=3 (in some cases,N=4). Binding energies, rms radii, density distributions, and quadrupole moments are calculated and found to be in reasonable agreement with experiment. Large Hartree-Fock energy gaps are obtained. They prevent the pairing correlations considered from becoming effective in an HFB approach and from changing the HF ground-state properties appreciably. In non-selfconjugate nuclei, the Pauli principle, rather than the Coulomb interaction, yields large differences between the charge and mass distributions. A theorem on selfconsistent symmetries is proved. The coefficients of the HFB transformation turn out to be real, if time-reversal and angular momentum projection flip are selfconsistent symmetries.