Superfluid states in β-stable nuclear matter

Two superfluid states of nuclear matter, which are supposed to play an important role in neutron stars, are discussed: the first one due to the proton-proton ¹ S ₀ pairing in β-equilibrium nuclear matter; the second one due to the anisotropic neutron-neutron ³ PF ₂ pairing in neutron matter. Since the two phases appear at high density of nuclear matter, the three-body forces were added to the pairing interaction and the strong correlation effects in the single-paricle spectrum. The energy gaps, obtained solving the extended BCS equations, significantly deviate from the values without medium effects so as to limit the role of these two superfluid states in the interpretation of phenomena occurring in the neutron-star core.     

A possible mechanism for magnetar soft X-ray/γ-ray emission

Once the energies of electrons near the Fermi surface obviously exceed the threshold energy of the inverse β decay,electron capture(EC) dominates inside the magnetar.Since the maximal binding energy of the 3 P 2 neutron Cooper pair is only about 0.048 MeV,the outgoing high-energy neutrons(E k(n) > 60 MeV) created by the EC can easily destroy the 3 P 2 neutron Cooper pairs through the interaction of nuclear force.In the anisotropic neutron superfluid,each 3 P 2 neutron Cooper pair has magnetic energy 2μ n B in the applied magnetic field B,where μ n = 0.966 × 10 23 erg.G 1 is the absolute value of the neutron abnormal magnetic moment.While being destroyed by the high-energy EC neutrons,the magnetic moments of the 3 P 2 Cooper pairs are no longer arranged in the paramagnetic direction,and the magnetic energy is released.This released energy can be transformed into thermal energy.Only a small fraction of the generated thermal energy is transported from the interior to the surface by conduction,and then it is radiated in the form of thermal photons from the surface.After highly efficient modulation within the star’s magnetosphere,the thermal surface emission is shaped into a spectrum of soft X-rays/γ-rays with the observed characteristics of magnetars.By introducing related parameters,we calculate the theoretical luminosities of magnetars.The calculation results agree well with the observed parameters of magnetars.     

Nanocluster magnetic gel in superfluid He-II

The first results of the study of the structure of an impurity oxygen gel in superfluid He-II and in normal liquid helium have been obtained by the small-angle neutron scattering (SANS) method with cold neutrons. The angular dependence of the neutron scattering intensity I(q) indicates that the characteristic sizes of nanocluster aggregates forming a dispersive system (backbone) of an oxygen gel sample are distributed from 1 to ≈100 nm. According to the estimates made, if the working cell with superfluid helium cooled below 1.8 K is placed in a magnetic field of H ≥ 200 G, the magnetic structure of the nanocluster sample of oxygen gel, which is formed at the condensation of the flow of gaseous ⁴He with the impurity of O₂ vapor on the surface of He-II, will be close to ferromagnetic.     

Isomeric yield ratio of fission product148Pr in235U(n th,f)

The independent isomeric yield ratio of¹⁴⁸Pr in thermal neutron induced fission of²³⁵U has been determined experimentally. The fission product¹⁴⁸Pr isomers, extracted directly by on-line mass separation technique, have high-spin (J=4) to low-spin (J=1) isomer ratio of 0.14±0.04 using growth and decay analysis. Statistical model calculation of isomeric yeild ratio using constant initial r.m.s. angular momentumJ _rms can not reproduce either present results or other recent measurements of isomer ratios. TheJ _rms derived from isomer ratio data in all thermal fissioning systems indicate a wide spread ranging from 2? to 13?. No clear correlation betweenJ _rms and isomeric spins or number of neutrons of isomers is found, thus, more model refinements and experimental works should be done in order to evaluate independent isomeric yields correctly.     

Investigation of the pion condensation threshold in finite nuclei

The threshold condition for pionic instabilities in finite nuclei is investigated by evaluating the response function for pion-like nuclear excitations (i.e. isovectorJ ^π =0^?, 1⁺, 2^?, ... excitations). The onset of pion condensation is then defined as the point where the response function for givenJ ^π becomes infinite at frequencyω=0. Using a momentum space representation for the response function which allows to establish clear connections to the nuclear matter case, we find that for angular momentaJ smaller than a maximum value which depends on the size of the nucleus, the threshold condition is almost the same as for infinite matter. We also study the systematics of this phenomenon as a function of nuclear mass number.     

Gliding for Gold: The Physics of Winter Sports,by Mark Denny

A comparison of the basic properties of the superfluid phases of liquid ³He with those of electrons in Type I superconductors and of bosons in liquid ⁴He reveals their similarity and differences. This is followed by some examples of the liquid crystal and magnetic properties of superfluid ³He and an account of the relationships between the tensor order parameter and the collective modes of the superfluid phases. The article ends with some comments on our present understanding of quantum liquids.     

Gamma rays from resonance neutron capture in 115In

Gamma rays in the range 5.4–6.7 MeV have been studied for 31 s-wave neutron resonances of ¹¹⁵In, selected by time of flight in the range 3–430 eV. In a subsidiary experiment, spin J = 5 has been assigned to 17 and J = 4 to 14 resonances by measuring intensity variations of some strong low-energy transitions. The reduced widths averaged over all initial states of the same spin have been estimated for 41 primary transitions: these values have provided information on the spin and parity of the corresponding ¹¹⁶In final states. Overall mean values of E1 and M1 radiative strength have been calculated. The width distribution has been fitted with a χ² function with ν = 1.10^+0.27_?0.09 degrees of freedom for M1 and ν = 1.42 ^{+ 0.014}_?0.08 for E1 radiation. An estimate of the spin cut-off parameter σ = 3.6_?0.4^{+ 0.8} has been derived. A non-statistical effect already evidenced in previous measurements has been confirmed, consisting of a strong modulation of the radiative strength against resonance energy, correlated also with the local neutron strength function. In addition, it has now been shown that this structure is due to E1 radiation only.     

The 6− analog-antianalog states of 28Si

A resonance is observed in the ²⁷Al(p, γ)²⁸Si reaction at E_p=2876±2 keV, which corresponds to an excitation energy of 14356±2 keV. The 14.36 MeV level decays to a new level at 11577±2 keV, which is turn decays to the known level at 9701.8±0.5 keV. With previous information on the 9.70 MeV level and the present γ-ray angular distributions, obtained from singles spectra as recorded by a 40 cm³ Ge(Li) detector, the spins of the three levels can be limited to J=5, 6; J=6; and J=5, respectively. Transition strength arguments based on measurements of the strength of the 2876 keV resonance and the lifetime of the 11.58 MeV level indicate that the 14.36 MeV level has J^π=6^?, T=1 and that the 11.58 MeV level has J^π=6^?, T=0.     

Triplet superfluidity in neutron matter with Skyrme forces at subnuclear and supranuclear densities in a strong magnetic field

Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T _c,1(n, H) and T _c,2(n, H) (which are nonlinear functions of density, n, and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases ³He - A₁ and ³He - A₂) in steady and homogeneous sufficiently strong magnetic field (but |μ _n |H ≪ E _c < ɛ _F (n), where μ _n is the magnetic dipole moment of a neutron, E _c is the cutoff energy and ɛ _F (n)is the Fermi energy in neutron matter). General formulae for T _c,1,2(n,H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density n (at sub- and supranuclear densities) from the interval 0.7 n ₀ ≲ n < n _c (Skyrme)< 2 n ₀, where n ₀ =0.17 fm⁻³ is the nuclear density and n _c (Skyrme)is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.     

Combining a langevin description of heavy-ion induced fission including neutron evaporation with the statistical model

A model is developed which combines dynamical (Langevin-) calculations with the Kramers modified statistical model in order to describe heavy-ion induced fission including neutron evaporation. In the example of the¹⁹F+¹⁸¹Ta collision, the energy dependence of fission probabilities, neutron multiplicities and (H.I.,xn)-cross sections is calculated and a fair agreement with the data is achieved with a reduced friction parameter ofβ=3^*10²¹sec^?1. We pay particular attention to the angular momentum dependence of the fusion-fission process.     

Resonances in low energy40Ca(α, α)-scattering and quasimolecular band in44Ti

The elasticα-scattering from⁴⁰Ca has been studied betweenE _α=7.035 MeV and 7.405 MeV. Angular distributions and excitation functions have been measured in 5 keV steps. The data display a resonance atE _α=7.26 MeV which by its width and angular correlation is clearly distinguished from strong Ericson fluctuations in this region. From the analysis of the angular distributions and excitation functions a spinJ ^π=1^? is assigned to this resonance. The resonance parameters areΓ _α=31 KeV,Γ _total=51keV. By its spin and excitation energy this state is interpreted as a member of a quasimolecular band in⁴⁴Ti the higherl-members of which are known from⁴⁰¹Ca(α, α) scattering betweenE _α=18 MeV and 50 MeV. The experimental data are compared with recent microscopic calculations within a fully antisymmetrized reaction theory.     

Dominance of α decay from the isoscalar giant quadrupole resonance in 16O

The charged particle (c) decay of the isoscalar giant quadrupole resonance in a ¹⁶O has been studied in a ¹⁶O(α,α'c) coincidence experiment at E_α=155 MeV. The J=2 character of this resonance was established by angular correaltion measurements. Its dominant decay proceeds through the α₁ channel which contains about 40% of the E2 energy weighted sum rule. This explains difficulties of capture reactions to locate the GQR.     

Variational Calculation of Energies of Highly Excited Rovibrational States of CO2

Accurate variational calculations of energies of highly excited rovibrational states of ¹²C¹⁶O₂ using a Lanczos recursion are presented. In a first step, we use experimental rovibrational transition frequencies to determine by a least-square fitting procedure a potential energy surface for the CO₂ molecule. This potential energy surface is expressed as a multidimensional power series expansion in the normal coordinates. It is then used to determine all the rovibrational energies for symmetry e levels up to a rotational number J=200, a vibrational energy of 13 000 cm⁻¹, and a vibrational angular momentum l=13.     

A study of the121,123Sb(p,d) reactions

Levels of^120,122Sb have been observed using the^121,123Sb(p, d) reactions atE _p = 26.2 MeV. Thirty-two levels of¹²⁰Sb and thirty-four levels of¹²²Sb are observed below 2.0 MeV excitation with an energy resolution better than 25 keV FWHM. Experimental angular distributions were compared to DWBA calculations in order to extractl-transfers and spectroscopic factors. Strong mixing between the 3s _1/2, 2d _3/2, 2d _5/2, and 1g _7/2 neutron orbitals is observed in both nuclei. Nuclear Reactions:^121,123Sb(p, d),E=26.2 MeV; measuredσ(E _d ,θ).^120,122Sb deduced levels,l,J,π, spectroscopic factors. Enriched targets, magnetic spectrometer.     

Rectification of the dipole force in a monochromatic field created by elliptically polarized waves

The rectification of the force of induced light pressure in laser fields formed by elliptically polarized running waves in zero magnetic field is considered. Explicit analytic expressions for the induced and spontaneous forces of light pressure exerted on a stationary atom are obtained for two classes of closed optical transitions: J _g=J→J _e=J+1 and J _g=J→J _e=J (J is half-integral), where J _g and J _e are the total angular momenta of the ground and excited energy levels. It is shown that the ellipticity of waves is the necessary condition for the emergence of the rectification of the induced force in a monochromatic field. The optimal parameters of the field and the maximum rectification coefficient are calculated for a number of optical transitions. The dependence of the rectified force on the velocity is investigated analytically and numerically for the simplest 1/2→1/2 transition.     

Deformed states of high spin in42Ca

The⁴²Ca levels at 4,715 and 6,633 keV excitation energy have been investigated using the³⁹ K(α,pγ reaction atE _α=14 and 15 MeV. From particle-γ-ray angular correlations the spin assignmentsJ(4,715)=6, 4 andJ(6,633)=8, 6, 4 have been obtained. Lifetime measurements using the Doppler-shift attenuation method yieldedτ (4,715)=120±46 fs andτ(6,633)=52±21 fs. Both levels have positive parity and decay by enhancedE2 transitions. They are interpreted as theJ ^π=6⁺ and 8⁺ members, respectively, of theK ^π=0⁺ rotational band which has theE _x =1,837, 2,423 and 3,250 keV states as further members. The enhancement of inbandE2 transitions is 50 _?16 ⁺³⁵ W.u. (6→4) and 63 W.u. (8→6) respectively. The intrinsic quadrupole moments which have been derived on the basis of the coexistence model, areQ ₀=1.13?0.16/+0.37b(8→6) andQ ₀=1.36±0.25b(6→4), respectively. TheJ ^π=10⁺ member of the rotational band has possibly been observed as a level at 8,856±5 keV excitation energy.     

The gamma decay of analogue states in61Cu

Resonances in the reaction⁶⁰Ni(p, γ)⁶¹Cu have been studied in the proton energy rangesE _p=1840–1880 keV and 2220–2300 keV. Decay schemes and branching ratios have been determined for a number of resonances, three of which are identified as analogue fragments of the 283 keV (1/2^?) and 656 keV (3/2^?) states in⁶¹Ni. The split analogue components of the 283 keV state atE _x≈6.6 MeV are seen to decay significantly to a group of states in the region of excitation 3–4 MeV. Gamma ray angular distributions yield the following resonance spins:E _p=2248 keV,J=3/2;E _p=2263 keV,J=5/2. Also, the⁶¹Cu ground stateβ ⁺ decay to parent levels in⁶¹Ni has been compared to the respective analogue stateM1 gamma decay to the⁶¹Cu ground state.     

Excitation of the analogue of the T> giant dipole resonance of90Zr via the (n,p) reaction

Proton spectra have been measured at lab angles ofθ=0° to 100° for the reaction Zr(n, p)Y at 21.8 MeV incident neutron energy. Spectra over an angular spread of 80° were accumulated simultaneously using a detection system consisting of proportional counterΔE detectors and a curved plastic scintillator as energy detector. Resonant behaviour is observed in the proton spectra for the Zr(n, p)Y reaction but not for the Fe(n, p)Mn reaction. The resonant structure is attributed to the excitation of the analogues ofT _> giant dipole states of Zr. The resonant structure is shown to correspond in position, gross and fine structure, and, in strength and angular dependence of the cross sections, with expectations for the⁹⁰Zr(n, p)⁹⁰Y reaction. DWBA cross sections are derived and fitted to the experimental data with a Lane potential of 150 MeV.