Quadratic spin-orbit forces and the deuteron magnetic moment

The contribution to the deuteron magnetic moment due to L-dependent components of the two-nucleon force is discussed and evaluated for several potential models. The Reid soft core potential is expressed as a sum of central, tensor, spin-orbit, L² and Q₁₂ forces and it is argued that this choice of components has a number of advantages.     

The decay of the neutron deficient plutonium isotopes 232, 233 and 234

The plutonium isotopes²³²Pu,²³³Pu and²³⁴Pu were produced by (α,xn) reactions with²³³U. After a chemical separation their decay was studied by γ-ray and α-spectros-copy. For²³³Pu twenty-seven γ-ray energies and intensities were measured and a decay scheme is proposed. An additional α-transition was detected for²³²Pu. The half-lives were determined for all three isotopes.     

Photofission of 238Pu, 240Pu, and 242Pu in the energy range 5–10 MeV

The cross sections for the photofission of plutonium isotopes ²³⁸Pu, ²⁴⁰Pu, and ²⁴²Pu in the energy range 5–10 MeV have been measured by using a beam of bremsstrahlung photons from the microtron installed at the Institute of Physics and Power Engineering (Obninsk). The energy regions below the fission barrier and above 6 MeV have been scanned with pitches of 0.05 and 0.1 MeV, respectively. In deriving the absolute cross section for ²³⁸Pu photofission, ²³⁸U photofission has been employed as a reference reaction. In measurements involving ²⁴⁰Pu and ²⁴²Pu nuclei, the neptunium isotope ²³⁷Np, which is characterized by a more regular dependence of the photofission cross section on excitation energy than ²³⁸U, has been chosen for the first time as a reference nucleus. The measured cross sections as functions of energy show resonance structures in the vicinity of the fission threshold that are consistent with those previously observed in the energy dependences of fissilities for corresponding direct reactions. The partial-wave cross sections for the J ^π K = 1^?0, 1^?1, and 2⁺0 photofission channels have been determined as functions of energy. At energies below some 5.5 MeV, the total cross section for photofission of each plutonium isotope being studied receives a significant contribution from quadrupole interaction. Within the one-dimensional model of a two-humped fission barrier, the parameters of the barriers for ²³⁸Pu, ²⁴⁰Pu, and ²⁴²Pu have been extracted from data and have then been compared with estimates based on previous measurements.     

Resonances in the isomeric and prompt fission probabilities of240Pu

The prompt and isomeric fission probabilities of²⁴⁰Pu have been studied using the²³⁹Pu(d,p) reaction. A number of resonances are observed in the subbarrier population of the 4 ns fission isomer for excitation energies between 4.0 and 6.2 MeV. Apart from a structure at 4.3 MeV, they do not coincide with transmission resonances found in prompt fission. Calculations with an extended doorway state model which simultaneously reproduce the measured delayed and prompt fission probabilities yield revised fission barrier parameters as well as spectroscopic information on fission and gamma widths of highly excited states in the second minimum.     

Magnetic moments and GT-type β-decay matrix elements in nuclei with a LS doubly closed shell plus or minus one nucleon

The magnetic moments and GT-type β-decay matrix elements of nuclei with an ¹⁶O core plus (minus) one nucleon and with a ⁴⁰Ca core plus(minus) one nucleon are studied from the point of view of configuration mixing in terms of second order perturbation theory. It is found that the effect of the mixing of highly excited configurations through a tensor force is essential to explain the large reduction of the GT-type β-decay matrix elements. It is also found that modulus of the isovector parts of the gyromagnetic ratio, g_τS and g_τl, are appreciably reduced by the configuration mixing.     

Vibrational resonances below 5 MeV in the fission of 240Pu

Using the ²³⁹Pu(d, pf) reaction, the next lower K^π = 0⁺ vibrational resonance below 5 MeV in the deformed potential of ²⁴⁰Pu was located at 4.55 MeV. The resultant spacing of fission vibrations near 5 MeV in the second minimum is 500 keV. A resonance at 4.70 MeV is interpreted as the K^π = 0^? vibration coupled to the 4.55 MeV K^π = 0⁺ state, which yields E(K^π = 0^?) = 150 keV relative to the ground state of the second minimum.     

Fission accompanied by alpha particle emission in the12C(85MeV)+232Th reaction

Inclusive and coincident spectra of alpha particles and fission fragments were measured for the²³²Th+¹²C (85 MeV) reaction to study the influence of the excitation energy and the angular momentum on the fission of the compound nucleus and to separate different alpha particle emission mechanisms. At backward angles α emission can be accounted for by the evaporation processes. At forward angles the most important contribution is given by the break-up fusion process. Mass distributions for compound nuclei²⁴⁴Cm (E^*=58 MeV,ff coincidences), and²⁴⁰Pu (E^*=37 MeV,ff α coincidences) were obtained. In the case of²⁴⁰Pu mass distribution has a shape different from those obtained in light ion reactions at the same excitation energy, indicating the strong influence of the entrance channel. The dependence of the mass distribution shape on the α particle energy is also examined.     

Correlations between potentials and observables in the NN interaction

We study the effects of the components of the soft-core and velocity-dependent Paris nucleon-nucleon potential on the scattering observables for laboratory energies, T_L, between 10 and 350 MeV. Knowledge of these correlations is useful to indicate constraints on components of the nucléon-nucléon force. The velocity-dependent component, attractive at low energy and repulsive at high energy, plays a role at all energies. The polarisation P, the depolarisation D and the parameters D_t, A, R, C_KP and C_NN are good tests for the tensor, spin-orbit and, to a smaller extent, quadratic spin-orbit forces. The isovector tensor force contribution is important at low energy and that of the isovector spin-orbit at high energy. The isoscalar tensor force effect is large at all energies and that of the isoscalar spin-orbit force rather small. The potential without quadratic spin-orbit term reproduces well the experimental data for T_L < 150 MeV.     

Tensor Force Manifestations in ab Initio Study of the 2H(d, γ)4He, 2H(d, p)3H, and 2H(d, n)3He Reactions

The ²H(d, γ)⁴He capture reaction and the ²H(d, p)³H and ²H(d, n)³He transfer reactions at very low energies are studied in an extended microscopic cluster model with a realistic nucleon–nucleon force. Our results show that the tensor force in realistic interactions plays an essential and indispensable role to reproduce the very low-energy astrophysical S factor of these reactions.     

Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism

The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.     

Self-consistent calculation of the fission barrier of 240Pu

Completely self-consistent calculations using the Skyrme force have been carried out for the fission energy curve of ²⁴⁰Pu. We use a deformed oscillator basis including 13 major shells and convergence has been checked by extending the size of the basis to 15 shells. We obtain a double humped barrier with energies E_A = 9 MeV for the first barrier, E_B = 13 MeV for the second barrier and E_II = 4 MeV for the isomeric state. Corrections to our calculation, such as inclusion of non-axial and symmetric shapes and zero-point rotational motion, are likely to improve quantitative agreement with experimental data.     

Puzzle of the <Superscript>6</Superscript>Li quadrupole moment: Steps toward solving it

The problem of the origin of the quadrupole deformation in the ⁶Li ground state is investigated with allowance for the three-deuteron component of the ⁶Li wave function. Two long-standing puzzles related to the tensor interaction in the ⁶Li nucleus are known: that of an anomalous smallness of the ⁶Li quadrupole moment (being negative, it is smaller in magnitude than the ⁷Li quadrupole moment by a factor of 5) and that of an anomalous behavior of the tensor analyzing power T_2q in the scattering of polarized ⁶Li nuclei on various targets. It is shown that a large (in magnitude) negative exchange contribution to the ⁶Li quadrupole moment from the three-deuteron configuration cancels almost completely the “direct” positive contribution due to the αd folding potential. As a result, the total quadrupole moment proves to be close to zero and highly sensitive to fine details of the tensor nucleon-nucleon interaction in the ⁴He nucleus and of its wave function.     

New approximation of the energy dependences of total cross sections for proton-induced fission of actinide nuclei

The energy dependences of the cross sections for the fission of ²³²Th to ²³⁹Pu nuclei that is induced by protons of energy in excess of 50 MeV are proposed to be approximated by the sum of two functions. Of these, the first decreases exponentially with increasing proton energy. It represents the contribution of two-step fission, which competes with particle evaporation. The second function decreases exponentially as the energy grows to about 200 MeV, whereupon it increases up to an energy of 1 or 2.5 GeV. After that, it again decreases for ²³²Th to ²³³U nuclei or remains nearly unchanged for ²³⁷Np and ²³⁹Pu nuclei. This function is likely to represent the sum of the contributions from three modes of single-stage fission.     

The vector and tensor exchange contributions to πN → πN

Using fixed-t dispersion relations together with experimental data on π^?p → π⁰n we determine the real and imaginary parts of the s-channel helicity amplitudes (SHA) of the vector (?) exchange contribution to πN → πN. The results are in good agreement with amplitude analyses. We also make comparison with finite-energy sum-rules (FESR) and discuss certain implications. Furthermore, on the basis of two-component duality and FESR we calculate the tensor (f) contribution. The t-structure of the resulting SHA is compared with independent information on hadronic tensor exchanges.     

Investigations of the g factors for the trigonal [Ti(H2O)6] clusters in frozen solution from two microscopic spin Hamiltonian methods

The spin Hamiltonian parameters (SH) (g factors g_∥ and g_⊥) for the trigonal [Ti(H₂O)₆]³⁺ clusters in the rapidly frozen solutions of Ti³⁺ are calculated from the complete diagonalization (of energy matrix) method (CDM, which is established in this paper) and the perturbation theory method (PTM). The two methods are based on the two-spin-orbit-parameter model (where both the contribution due to the spin-orbit (SO) coupling parameter of central 3dⁿ ion and that of ligand are included) rather than the one-SO-parameter model in the conventional crystal-field theory (where only the contribution due to the SO coupling parameter of 3dⁿ ion is considered). The calculated results from both methods are not only consistent with the observed values, but also close to each other. This suggests that both methods can be effective in the studies of SH parameters.     

Meson exchange and the theory of finite fermi systems

The spin-dependent parameters g₀ and g'₀ in Migdal's theory of finite Fermi systems are studied. Assuming their values to be such as to reproduce the M1 states in ²⁰⁸Pb at 7 and 8 MeV, the origin of these (large) values in meson-exchange contributions to the nucleon-nucleon force is studied. Pion exchange contributes little, because of cancellation between matrix elements from the spin-spin and tensor components. The largest, nearly equal, contributions to g₀ and g'₀ come from p-meson exchange. In order to explain the large values needed for g₀ and g'₀, the tensor coupling of the ρ-meson must be substantially larger than the effective ones found in current phenomenological potentials, such as the Reid soft-core and Hamada-Johnston ones. The large value of the coupling needed follows from work analyzing nucleon form factors.     

Phenomenological renormalization of free nucleon-nucleon interaction

Low-lying spectra of⁶Li,¹⁸F,¹⁸O,⁴²Sc,⁴²Ca,⁵⁸Ni and⁹²Zr are studied with Sussex matrix elements (SME) and their central, spin-orbit and tensor components. It is observed that major contribution to level energies comes from the central part, while the tensor part provides the finer details of spectra, particularly forT=0 levels. The spin-orbit part does not make any appreciable contribution to level energies. A phenomenological renormalization of the SME is carried out to improve the agreement with the experimental results. It turns out that some of the low-lyingT=0 levels can be satisfactorily described if the SME in the³S₁ relative state are made (1+α) times their bare interaction value, whereα is a constant to be determined from a comparison with experimental level energies. Similarly, forT=1 levels, better agreement with the experimental results is obtained if aδ-function-plus-quadrupole interaction is added to the SME.     

Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.     

Antiferromagnetic hall effect nonlinear in the electric current

A new galvanoantiferromagnetic effect is predicted—the Hall effect nonlinear in the electric current, i.e., a potential difference that is transverse to the current and is associated with the antisymmetric contribution to the resistivity tensor, which violates Ohm’s law, for example, of the form Δρij=?Δρji∝LE, where L is the antiferromagnetism vector and E is the electric field. The indicated contribution is characteristic for centrally antisymmetric antiferromagnets and can lead to a Hall field that is quadratic in the current: ΔE ^⊥ ∝ LJ ². Similarly, the effect ΔE ^⊥∝LJ ³ can exist in centrally symmetric antiferromagnets even in a state where the ordinary Hall effect, which is linear in J, is absent (for example, in hematite below the Morin point).