Reaction mechanisms in the six-nucleon system with the multi-configuration resonating-group method

The properties of the six-nucleon system are examined with a multi-configuration resonating-group method consisting of thed+ configuration, thep+⁵He andn+⁵Li configurations, and deuteron pseudo-inelastic configurations. The main purpose is to study the reaction mechanisms in this system. The results obtained are quite satisfactory, with the calculatedd+ total reaction cross sections equal to around 90% of the empirically determined values. The one-nucleon transfer process turns out to be significantly more important than the deuteron direct-breakup process; however, the latter process must still be properly taken into consideration, since it does contribute to about one third of thed+ total reaction cross section. The process of one-nucleon transfer is shown to occur mainly in the peripheral region, while the process of deuteron direct-kreakup is found to take place predominantly in the interior region of the compound nucleus. The convergence property with respect to the number of deuteron pseudo-inelastic configurations has also been investigated. Here it is found that, with the dominant configurations included, the number of such configurations required can be rather small, which is an important finding because it greatly simplifies the computational aspects of multi-configuration resonating-group calculations.     

Resonating-Group Study of Three-Nucleon Bound State and p+d Scattering

The multi-configuration resonating-group method is employed to study the properties of the three-nucleon system. The model space is spanned by p+d, p+d', n+ 2p, and a large number of their associated pseudo-inelastic configurations. The nucleon-nucleon potential used is the Minnesota potential which contains nuclear central, Coulomb, and spin-orbit components. The results show that the calculated p+d complex phase shifts agree well with the values obtained by an empirical analysis of experimental data. Differential scattering and total reaction cross sections in the p+d system are calculated at centre-of-mass energies up to 32 MeV. Without adjusting any parameter, it is found that the agreement between calculation and experiment is quite satisfactory. The effects of successively enlarging the model space have also been examined. Here the finding is that, in order to obtain reliable results, all three types of cluster configurations must be included in the calculation. Received March 11, 1994; revised June 17, 1994; accepted for publication August 6, 1994     

Nonadiabatically Coupled Hyperspherical Equations Applied to the Collisional Spin Flip of Muonic Hydrogen

Nonadiabatically coupled equations in terms of hyperspherical coordinates are solved for the elastic and hyperfine transitions F→F′ of muonic hydrogen isotopes pμ, dμ, and tμ in collisions pμ(F)+p→p+μp(F′), dμ(F)+d→d+μd(F′), and tμ(F)+t→t+μt(F′), as an extension of our previous work on pμ [Igarashi et al., Phys. Rev. A 58 (1998), 1166]. Converged cross sections are obtained for collision energies 10^?3 to 10² eV and for the total orbital angular momentum L=0 and 1 including the spin–spin interactions V _S explicitly in the Hamiltonian, and for L≥2 neglecting V _S because of the large interparticle separations. The inclusion of V _S for L=0 and 1 reproduces the correct hyperfine-splitting energy Δ∈ in the separated-atom limit, and is found to be of vital importance for the calculation of the spin-flip cross sections for collision energies lower than Δ∈.     

Isospin-forbidden d1 production in the 4He(d,pαn reaction with tensor-polarized beam

The ${}^4\text{He}\text{(}\text{d}\text{,}\text{p}\text{α)}\text{n}$ reaction has been studied in a kinematically complete experiment using a tensor-polarized deuteron beam to investigate the isospin-forbidden pn final-state interaction. A clear dependence of the cross section near E_pn = 0 on the spin state of the incoming deuterons has been found as expected if the bumps observed by several authors at small pn relative energies are indeed due to the isospin-forbidden proton-neutron FSI in the ¹S₀, T = 1 state.     

Calculations of electron screening in muonic atoms

The electron screening in mounic atoms (O, Al, Fe, In, Ho, Au, Th) has been calculated forp _3/2,d _5/2 andf _7/2 levels withn _µ≦30 and for circular orbits withn _µ≦12 using a relativistic Dirac-Fock program. Simple empirical formulae are presented which can be employed to calculate the screening corrections for all elements fromZ=8 toZ=90, forp _3/2,d _5/2 andf _7/2 muons up ton _µ=30 Screening corrections are also given for electron configurations with holes in theK andL ₃ shell.     

Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0

This paper investigates infinite-time spreading and finite-time blow-up for the Keller-Segel system. For 0 < m ≤  2 ? 2 / d, the L ^p space for both dynamic and steady solutions are detected with ${p:=\frac{d(2-m)}{2} }$ p : = d ( 2 - m ) 2 . Firstly, the global existence of the weak solution is proved for small initial data in L ^p . Moreover, when m > 1 ? 2 / d, the weak solution preserves mass and satisfies the hyper-contractive estimates in L ^q for any p < q < ∞. Furthermore, for slow diffusion 1 < m ≤  2 ? 2/d, this weak solution is also a weak entropy solution which blows up at finite time provided by the initial negative free energy. For m > 2 ? 2/d, the hyper-contractive estimates are also obtained. Finally, we focus on the L ^p norm of the steady solutions, it is shown that the energy critical exponent m = 2d/(d + 2) is the critical exponent separating finite L ^p norm and infinite L ^p norm for the steady state solutions.     

Spin selectivity of the polarised (d, 2p) reaction

Tensor polarisation observables in intermediate energy $\text{(}\text{d}\text{, 2}\text{p}\text{)}$ charge exchange on 0⁺ nuclei are investigated. It is shown that for small excitation energies of the di-proton the polarisation can help to distinguish between 0^?, 1^? and 2^? final nuclear states produced through ΔL = 1, ΔS = 1 transitions. The information to be obtained is similar to that inherent in $\text{(}\text{p}\text{,}\text{n}\text{)}$ spin transfer experiments but the deutron-induced experiments should have much higher efficiency.     

High-spin states in26Mg

Theγ-decays of levels in²⁶Mg have been investigated up to 12.5 MeV excitation energy by proton-γ-ray coincidence measurements in the²³Na(α, pγ) reaction at 14.2 and 16 MeV bombarding energy. Lifetime-measurements, made with the Doppler-shift attenuation method, and proton-γ-ray angular-correlation measurements were performed at E_α=14.2 MeV. Many high-spin states were observed, among them levels at 6,978 (5⁺), 7,283(4^?), 7,395(5⁺), 7,953(5^?), 8,202(6⁺), 8,472(6⁺), 9,065(5), 9,112(6⁺), 9,169(6^?), 9,383 (6⁺), 9,542(5), 9,829(7⁺), 9,989(6⁺) and 12,479(8⁺, 7^?) keV excitation energy. The spectrum of positive-parity states and their electromagnetic properties are reproduced with good accuracy by shell-model calculations which employ a unifieds-d shell Hamiltonian and the unrestricted configuration space of the 0d _5/2 1s _1/2 0d _3/2 shell. Members of five inferred rotational bands, withK ^π=0⁺, 2⁺, 3⁺, 0⁺ and 3^? have been observed up to at leastI=6. TheK ^π=2⁺ band shows strong anomalies of excitation energies andE2 transition rates near theI=6 state. The static intrinsic quadrupole moments calculated from the shell model wave functions indicate transitions from prolate to oblate deformation within theK ^π=2⁺ band and also the ground state band. The lowest lyingI ^π=4⁺ state appears to be “spherical” and cannot be associated with a rotational band.     

Theory of the muonic hydrogen-muonic deuterium isotope shift

Corrections of the α³, α⁴, and α⁵ orders are calculated for the Lamb shift of the 1S and 2S energy levels of muonic hydrogen μp and muonic deuterium μd. The nuclear structure effects are taken into account in terms of the charge radii of the proton r _p and deuteron r _d for one-photon interaction, as well as in terms of the electromagnetic form factors of the proton and deuteron for the case of one-loop amplitudes. The μd-μp isotope shift for the 1S-2S splitting is found to be equal to 101003.3495 meV, which can be treated as a reliable estimate when conducting the corresponding experiment with an accuracy of 10^?6. The fine-structure intervals E(1S)-8E(2S) in muonic hydrogen and muonic deuteron are calculated.     

Core polarization and 5/2+ states in91Nb

The energies and spectroscopic factors ofJ ^π=5/2⁺ states of nucleus⁹¹Nb excited via a reaction transferring a proton to the 2d _5/2 orbit of⁹⁰Zr target state have been calculated. Effective two-body interaction used has been extracted from the experimentally observed two-body energies of (1g ₉ ^2/?1 (n) 2d _5/2(n)), (1g ₉ ^2/?1 (n) 1g _9/2(p)) and (1g _9/2(p)-2d _9/2(n)) multiplets in⁹⁰Zr,⁹⁰Nb and⁹²Nb nuclei respectively. Most of the calculated energies and the strengths ofJ ^π=5/2⁺ levels have reasonably good counterparts in the experimental spectrum, however the calculation shows about 17% strength lying at 6.8 MeV, without having a confirmed counterpart in the observed level scheme. The reduced transition strengthsB(M1) forM l transitions from 5/2^? T>(11/2) state to the various components of 5/2⁺ T<(=9/2) state have also been reported; but the corresponding experimental values are not available. The main feature of the reduced transition strengths is that theM1 transition to the state at 3.69 MeV is inhibited whereas that to the state at 6.79 MeV is enhanced, the relevant core-configuration, interfering destructively in the former case and constructively in the latter.     

Analysis of the spectra of In XII–XIV and Sn XIII–XV in the far-VUV region

The 4p ⁶4d?(4p ⁶5p + 4p ⁶4f + 4p ⁵4d ²) transitions in the spectra of In XIII-Sn XIV and the 4p ⁶4d ²?(4p ⁶4d5p + 4p ⁶4d4f + 4p ⁵4d ³) transitions in the spectra of In XII-Sn XIII are investigated. About 150 spectral lines in the wavelength range 120–160 Å, which is important for projection vacuum UV lithography, have been classified for the first time. The fine structure intervals of the ground state 4p ⁶4d ² D and the energies of eight levels of the 4p ⁶5p, 4p ⁶4f, and 4p ⁵4d ² configurations are measured in each spectrum of In XIII and Sn XIV. The energies of all levels of the ground configuration 4p ⁶4d ² and the energies of 35 levels of the interacting configurations (4p ⁶5p + 4p ⁶4f + 4p ⁵4d ³) are determined in the spectra of In XII and Sn XIII. The resonant transitions 4p ^{6 1} S ₀?4p ⁵4d ¹ P ₁ in the spectra of In XIV and Sn XV are also identified. The semiempirical parameters of the configurations under study determined by mean-square fitting of measured level energies are in agreement along both isoelectronic and isonuclear sequences of the spectra.     

The deuteron D-state probability

A method of direct determination of the deuteron D-state probability from the experiment, based on thed ↑p →ppn reaction analyzis is suggested. Using the known results on the vector analyzing power in elasticN N-scattering, the values of the overall nucleon polarization and the deuteron vector polarization have been obtained. The probability of the deuteron D-state is estimated to beW _D =0.078±0.046.     

Structure of the mirror nuclei21Ne and21Na

Theγ-decay of levels in²¹Ne up to 10 MeV excitation energy has been investigated byn — γ coincidence measurements initiated with the¹⁸O(α, nγ) reaction at 12, 13, 14.5 and 15.4 MeV bombarding energies. Spin(-parity) assignments of excited states are obtained by combining then — γ angular correlation measurements performed atE _α=11, 11.82 and 13.6 MeV with a consideration of lifetimes, neutron penetrabilities of the unbound states, and information from the mirror nucleus²¹Na. The resulting values of E_x[keV]?J ^π are as follows: 4525-5⁺, 4686-3⁺, 5431-7⁺, 5549-3⁺, 5819-7^?, 6175-7⁺, 6268-9⁺, 6550-9, 6639-9, 7006-7⁺, 7041-9, 7356-7 or 9, 7422-11^(?), 7648-7⁺, 7981-11 or (7⁺), 8154-9, 8240-11, 8664-9^? or 11 or 13^?, 9401-13^?, 9867-13^? or 15⁺, 9941-13^? or 15 or 17⁺. The assignment of mirror levels in²¹Ne —²¹Na has been extended to the 6175 keV level of²¹Ne. Excitation energies, electromagnetic properties, Gamow?Teller matrix elements and spectroscopic factors of positive parity states are compared with the results of shell-model calculations which employ a unifieds—d shell Hamiltonian and the unrestricted configuration space of the 0d _5/2 —1s _1/2—0d_3/2 shell. Collective properties contained in shell model wave functions are explored up to the termination of bands atJ=17/2 or 19/2. The spectrum of intruder states in²¹Ne is observed to begin with a 5628 keV,J ^π=7/2⁺ state. The 7422, 8664 and 9401 keV levels are assigned as members of previously established negative-parity rotational bands.     

Strong spin-dependent absorption at theL 2,-edges of 5d-impurities in iron

Large spin-dependent absorption effects have been observed with circularly polarized photons of energies between 10.8 keV and 13.8 keV at theL _2,3-edges of Os, Ir, Pt, and Au impurities (3 at.%) in iron. The largest value of the spin-dependent absorption coefficient (µ _c /µ _o +0.22) is found at the PtL ₂-edge. From the energy dependence of the spin-dependent absorption at theL ₂- andL ₃-edges the spin-density profiles of thed _3/2-andd _5/2-projected states populated in the absorption process are derived. Thed _5/2-spin densities deduced from theL ₃ spin-dependent absorption spectra agree well with spin-polarized band-structure calculations for the ferromagnetic ground state. A comparison of thed _3/2- andd _5/2-spin densities shows a strong contribution of the spin-orbit effects to the exchange splitting in Os, whereas only small spin-orbit effects are indicated for Ir, Pt and Au impurities.     

Analysis of the3 He(K−,K +)n reaction by the potential quark model

We analyze the production of H dihyperson (J ^π=0⁺,S=?2) via the (K ^?, K⁺) reaction by means of the non-relativistic quark model. First, the H mass and mass spectrum of single baryons are calculated. When the single baryon spectrum is well reproduced, the H dihyperson has the binding energies about 20 MeV or 60 MeV corresponding to the choice of the strength of the confinement potential. Using this model and parameters, cross sections for H production are estimated. A new effect, contributions from color-octetQ ³?Q ³ components of H dihyperson, is taken into account. The cross sections for H production are enhanced about ten times by these contributions. TheK ⁺-neutron coincidence cross section for H production is found to be 99–115 nb/sr² at theK ⁺ forward direction forM _H=2212 MeV and theK ^? beam momentum 1.8 GeV/c.     

Influence of theD and6Li quadrupole moments on theD(α,γ)6Li stellar reaction rate

We have studied theD(α, γ)⁶Li reaction at stellar energies within a potential model. Our calculation improves previous investigations as we explicitely take into account the internal quadrupole moment of the deuteron and ad-state component in the⁶Li ground state. We reproduce the experimental data for energiesE<3 MeV. We find, however, that our improvements represent only minor corrections.     

Solution of the10Li-Puzzle

The mass of¹⁰Li has been measured with two different reactions:⁹Be(¹³C,¹²N)¹⁰Li,E _Lab=336 MeV, and¹³C(¹⁴C,¹⁷F)¹⁰Li,E _Lab=337 MeV. The mass excess of 33.445(50) MeV is deduced from theQ-value measurement.¹⁰Li is found to be particle-unstable with respect to one-neutron emission by 0.42(5) MeV. In the analysis of the first reaction a low lying excited state is found at 0.38(8) MeV. This state and the ground state can be most probably identified as the 1⁺/2⁺-doublet coupled from the [π 1p3/2 ?ν 1p 1/2] configuration, the 1⁺-state being the ground state. The (¹³C,¹²N)-reaction populates the 1⁺-state strongly due to a spin-isospin-flip character of the dominant part of the transition amplitude. The 2⁺-member corresponds to the mass given by Wilcox et al. A second excited state is observed at 4.05(10) MeV with a width of 0.7(2) MeV, it can be associated with theν 1d 5/2-strength. The second reaction is fully supporting the interpretation of the ground state doublet. The excited state at 4.05 MeV is not observed in this reaction and indeed it should not, because the reaction does not populate in first order excited neutron configurations. The levels are well described by mean field calculations including pairing correlations. The lowest resonance in the calculations is theν 1/2^?-configuration, whereas theν 1/2⁺-configuration shows at the neutron threshold a strong non-resonant contribution.     

Half-life and configuration of the 1/2+ intruder state in203Bi

The decay properties of theJ ^π=1/2⁺,E _exc=1,098 keV state in²⁰³Bi were studied. The state was populated via the²⁰⁴Pb(p, 2n) reaction and the activity was studied with the ion guide isotope separator on-line system IGISOL. The half-life of the 1/2⁺ state was measured to beT _1/2=303 ±5 ms. From this value the partial half-lives of the three depopulating branches 1/2⁺ →7/2^? (E3), 1/2⁺→5/2^? (E3 +M2) and 1/2⁺→9/2 _g.s. ^? (M4) were deduced. Since all the transitions are configuration forbidden in first order, a detailed study of second-order shell-model configuration mixing could be performed.     

Neutron polarizations from the9Be(d,n)10B and11B(d,n)12C reactions

Neutron polarization angular distributions were measured for the⁹Be(d,n)¹⁰B and¹¹B(d,n)¹²C reactions for deuteron energies of 5.47 and 5.34 MeV, respectively. Using neutron time-of-flight techniques, polarizations to eight states in¹⁰B and to six states in¹²C have been measured. Neutron polarization energy excitation functions for both reactions were measured for deuteron energies from 3.0 to 5.5 MeV in 0.25 MeV steps at 30° (lab). Distorted wave method calculations carried out to compare theoretical calculations against experimental results were not in good agreement with the data.     

Analysis of the spectrum of the Zn-like Kr VII ion: Highly excited 4<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">d</Emphasis> and 4<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">s</Emphasis> configurations

The spectrum of the Zn-like Kr VII ion, excited in a capillary discharge and recorded with a high resolution in the wavelength range of 300–1000 Å, was studied. Previously performed identification of the transitions from the levels of the 4s4f, 4s5s, 4s5p, and 4s5d configurations is confirmed and extended, and the energies of these levels are specified. The (4p ²+4s4d)?4p4d and (4p ²+4s5s)?4p5s transitions are identified for the first time, and the energies of all the levels of the 4p4d and 4p5s configurations are determined. The results of the analysis performed are confirmed by semiempirical calculations in terms of the Hartree-Fock method. These results are also shown to conform to the experimental data obtained for lighter ions of the Zn I isoelectronic sequence.