The boundary condition approach to nucleon-nucleon potentials and the calculation of the T- and K-matrices

It has been shown that the off-shell T- and K-matrices can be obtained by means of boundary conditions imposed upon the off-shell wave function only. When there is a potential outside the boundary condition radius the method proposed permits to deduce in a rather simple way a renormalized Lippmann-Schwinger equation. The S-components of the T- and K-matrices are considered in detail using a potential of the exponential type in the exterior region. For such types of potentials a rather effective method for factorizing the K-matrix is given. Parameter fits to the ¹S₀ and ³S₁ phases are presented.     

Measurement of the population of the4 P 5/2-state in Ar15+ by cascading processes

The population of the⁴ P _5/2-state in Ar¹⁵⁺-ions by cascading processes was measured. The corrected lifetime is (0.55±0.04) ns and is in very good agreement with the theoretical value of 0.56 ns. At a specific beam energy of 1.4 MeV/u the lifetime of the³ P ₂-state of Ar¹⁶⁺ is not influenced by cascading processes and is (1.44±0.08) ns. The energies of the³ P ₂ →¹ S ₀- and⁴ P _5/2 →² S _1/2-transitions are (3127.2±0.5) and (3090.0±0.7) eV, respectively.     

Reaction matrix for nonlocal potentials. I. Magic nuclei

The binding energies of⁴He,¹⁶O, and⁴⁰Ca are computed applying the Brueckner theory of the reaction matrix for the Tabakin and the Mongan nonlocal separable potentials. Binding energies (10 MeV/nucleon) obtained are substantially greater than similar values for the local Hamada-Johnston potential (approx. 4÷5 MeV/nucleon). Detailed comparison of reference and exact reaction matrices for both types of potentials (local and nonlocal) in the coupled³ S-³ D channel confirms the existence of a strong correlation between the magnitude of the matrix elements of the reaction matrix and the intensity of a tensor force. A similar correlation also exists in the¹ S ₀ channel between the magnitude of matrix elements of the reaction matrix and the singlet scattering length. A different off-shell behaviour of individual potentials plays also a certain role.     

Irreducible kernels and nonperturbative expansions in a theory with purem →m interaction

Recent results on the structure of theS matrix at them-particle threshold (m≧2) in a simplifiedm→m scattering theory with no subchannel interaction are extended to the Green functionF on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure ofF arounds=(mμ)² depending on the parity of (m?1)(ν?1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernelU which is the analogue of theK matrix in the two different parity cases (m?1)(ν?1) odd or even, and related local expansion ofF, for (m?1)(ν?1) even, in powers of σ_β ln σ(σ=(mμ)²?s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernelU. The links between the kernelU and Bethe-Salpeter type kernelsG of the theory are exhibited in both parity cases, as also the links between the above expansion ofF and local expansions, in the Bethe-Salpeter type framework, ofF _λ in terms of Feynman-type integrals in which each vertex is a kernelG and which include both dominant and subdominant contributions.     

A constraint on the off-shell effective range parameter in p-p scattering

Sauer has recently proposed fixing the zero-energy ¹S₀ state wave function as a means of constraining the off-shell behaviour of the N-N interaction. We propose as an alternative that the value of the off-shell effective range parameter I₀ be constrained. A value of I₀ = 13 ± 1 fm³ seems to be indicated if charge symmetry is required.     

Trinucleon properties with one-boson-exchange potentials

The Faddeev equations are solved for two OBE potentials, HMl and EHM′. The two potentials differ primarily by the fact that HMl fits the¹ S ₀ n-p scattering data, while EHM′ fits the¹ S ₀ low-energy parameters of the Reid soft-core (RSC) potential. They give essentially identical values for the³ S ₁?³ D ₁ physical observables. The triton binding energy (E _T) and the³He charge form factor (CFF) are calculated for each OBE potential and compared with those of the RSC potential. Listed in the order (RSC, EHM′, HMl), the results forE _T are (7.0, 7.2, 7.5) MeV, while the positions of the minimum of the CFF areQ _MIN ² =(13.9, 15.3, 15.5) fm^?2. The two OBE potentials give increased binding in the triton, while simultaneously increasingQ _MIN ² .     

Second-order quadrupole splittings of the95Mo NMR signal in Mo(CO)6 and their reduction by sample spinning

The lifetimes of higher lying¹S_0?,¹D_2?, and¹F ₃ ⁰ -levels and of the 5s 7s³S₁- and 5p^{2 3}P₁-state in the Sr I-spectrum have been measured by a time resolved registration of the fluorescent intensity. The¹S_0? and¹D₂-levels were populated selectively by a two step optical excitation using two pulsed dye lasers. In the case of the¹F ₃ ⁰ -levels and of the³S_1?,³P₁-states the first excitation step was performed by a discharge, for the second, selective step a pulsed dye laser was used. The agreement of the experimental results with theoretically obtained lifetimes is satisfactory only in some cases.     

Three-nucleon calculations without the explicit use of two-body potentials

Using as two-nucleon interaction input the ³S₁-³D₁ and ¹S₀ partial waves, the Faddeev equations are solved for the three-nucleon bound state. The ³S₁³D₁T-matrix is calculated from the Reid potential. Avoiding the usual potential fit, the ¹S₀T-matrix is directly continued off-shell and is constructed consistent with the ¹S₀ phase shift of elastic two-nucleon scattering. The off-shell part of the ¹S₀T-matrix is parametrized and with this parametrization the dependence of the three-nucleon bound-state properties is studied. As a result it is found that the binding energy varies only between 6.2 MeV and 6.8 MeV, while the minimum in the charge form factor for electron scattering from ³He lies between 12.9 fm^?2 and 18.7 fm^?2. The larger (smaller) ³He binding energy is accompanied by a ³He charge form factor whose minimum is at larger (smaller) momentum transfers.     

A separable potential model for S0 neutron-proton interaction

A two-term separable potential is proposed for the ¹S₀ neutron-proton interaction. This potential is very soft. Its off-shell behaviour is very similar to that of a local potential.     

Nucleon nucleon interaction potential from experimental phase shifts

As an application of the inverse scattering technique of Marchenko to nucleon nucleon interactions, thenp ¹ S ₀ partial wave potential is generated. Experimental phase shifts of the Virginia and Saclay group serve as input. The mathematically derived potentials are discussed in view of uncertainties of input phase shifts and they are compared with potentials from Reid and the Paris group. The analysis shows the variance of present nucleon potentials in the 0–1 GeV range.     

Parametrization of the 1S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.     

Half-shellT matrix for Coulomb-modified Graz separable potential

We construct a closed form expression for the off-shell Jost function for scattering by the Coulomb-distorted Graz separable potential and express it in the ‘maximal reduced form’. Our result is particularly suitable for numerical computation. We present a case study in support of this and examine the role of Coulomb interaction in thep — p half-shell scattering in the¹ S ₀ channel.     

On the spin-orbit splitting of the rare gas-monohalide molecular ground state

The spin orbit splitting of the molecular ground state of two atomsA(² P _{1/2, 3/2}) andB(¹ S ₀) is discussed. If the spin orbit matrix elements do not depend on the internuclear distance, it is sufficient to know any two of the three potentials of the ground state manifold. The third can then be calculated analytically. Data are presented for theA II 1/2 state of F+Ne; (F, Br)+(Ar, Kr, Xe); and Cl+Xe, as well as for theA I 3/2 state of HeNe⁺.     

Three-body scattering in configuration space

The asymptotic forms of the wavefunction and Faddeev components in configuration space are shown to determine uniquely the solutions of the Schrödinger or Faddeev differential equations for 2 → (2, 3) and 3 → (2, 3) processes. An antisymmetrized form of the Faddeev differential equation for three equivalent fermions is given and its angular analysis is performed in the general case of local potentials with tensor interaction for neutron-deuteron scattering. We describe a numerical method for solving the corresponding boundary value problem and apply it to scattering and break-up at E_n^1ab = 14.4 MeV in the doublet S state for the four local potentials of Malfliet and Tjon, Reid, de Tourreil and Sprung, and de Tourreil, Rouben and Sprung. For the three realistic potentials, elastic scattering amplitudes differ by 5%, and amplitudes for break-up in the two-neutron state ¹S₀ differ by less than 4%.     

Relativistic corrections and very small g-shifts in solids

The relativistic Breit-Margenau correction to the Zeeman-interaction has been calculated for a group of atoms in the periodic table with Herman Skillman wave functions and potentials. The results are applied to the S-state ions Mn²⁺ and Gd³⁺, to the F-center and V_k-center, and to the shallow donors in Si.     

Natural radiative lifetimes in the2S1/2 and2D5/2,3/2 sequences of aluminum

Natural radiative lifetimes have been measured for the 3s ² ns ² S _1/2 (n≦10) and 3s ² nd ² D _5/2,3/2 (n≦11) sequences of aluminum using pulsed laser excitation of an atomic beam. The investigated states were populated from the ground configuration using UV pulses of wavelength down to 210 nm produced by a Nd: YAG- or an excimer-pumped dye-laser system. TheS-state lifetimes increase regularily with increasing principal quantum number but this is not the case for theD sequence.     

The transition operator for depolarizing collisions

The transition operator accounting for changes of the Zeeman sublevels of a¹ P-state or closely spaced² P-states has been derived using the classical-path approximation. In a first order approach to the problem thep-state atom is assumed to enter the range of a foreign atom non-adiabatically fast until reaching the point of the closest distance. There it is assumed to stop for the entire collision time. During this time the molecular σ and π states suffer phase-shifts due to the interaction with the molecular electric field. Subsequently thep-state atom leaves the range of the foreign atom again non-adiabatically fast. TheT-operator hence derived gives rise to the so-calledm _j-selection rule. In a better approach thep-state atom is assumed to stop twice when passing the range of the foreign atom. From this approximation additional terms to theT-operator arise which characteristically account for ‘molecular coupling’ phenomena during the collision. Consequently, these terms violate the afore-mentionedm _j-selection rule.     

Franck-Condon factors and absolute transition probabilities for the if (B3Π0+-X1Σ+) transition

Improved spectroscopic constants have been used to calculate Rydberg-Klein-Rees (RKR) potentials and Franck-Condon factors for the IF(B³Π₀₊-X¹Σ⁺) transition. The Franck-Condon factors are generally in good agreement with previously calculated values, but differ by as much as 30% for transitions from higher levels of the B-state. Several experimentally measured relative transition moment functions have been evaluated and the best scaled, so that the total transition probability calculated for each B-state vibrational level, A(v'), matched measured values. The scaled function was then used to calculate individual transition probabilities, A(v',v), for the vibronic transitions.     

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.     

The vibrational relaxation time constant for theB v=0 level of XeCl

The vibrational relaxation time constant for theB _v=0 vibrational level of XeCl^* has been investigated by observing the coupling between theB _v=1 andB _v=0 vibrational levels under saturated lasing conditions. Based on this observation, estimates of the expected extraction efficiency from theB-state have been made.