Singlet Potentials Research Articles

Non-Abelian Debye screening. II. The singlet potential.

The problems encountered in an earlier attempt to compute the non-Abelian Debye screening mass are rectified by considering the correlation of the eigenvalues of the untraced Polyakov loop. This gauge-invariant function is free from color averaging and is shown to yield the singlet potential of a static quark-antiquark pair at finite temperature. A perturbative computation requires that the electrostatic potential ${A}_{4}$ be endowed with a gauge-symmetry-breaking vacuum expectation value, the occurrence of which would explain the breakdown of perturbation theory encountered in the earlier calculation. While the symmetry breakdown cannot reliably be seen perturbatively, its effects on perturbative calculations can be assessed. It is found that most perturbative results, even the supposedly well-established low-order ones, would be affected. This would take the study of the quark-gluon plasma well out of the reach of perturbation theory and make nonperturbative techniques indispensable even at very high temperatures.

Momentum space Faddeev calculation for N-d scattering below the breakup threshold.

Momentum space Faddeev equations for different models that also include the Coulomb force between two protons and a spin triplet nucleon-nucleon tensor force within an angular momentum approximation are solved at ${E}_{\mathrm{lab}=0.2}$ to 2.0 MeV. From a low energy expansion of the N-d S-wave phase shifts, effective range parameters are extracted. The Coulomb contribution to the relation between the trinucleon binding energy and doublet scattering length remains qualitatively unchanged when either the separable nucleon-nucleon tensor potential or the singlet potential is varied. All our doublet p-d S-wave effective range functions show a nonlinear behavior that can be ascribed to a pole connected with a virtual trinucleon bound state, whereas phase shift analysis rejects such a pole. The calculated p-d differential cross sections are roughly compatible with experiment, suggesting that phase shift analysis might not be accurate enough to detect the virtual bound state.

Velocity dependence for the chemi-ionization of Ar, Kr, N2, CO, and O2 by He(2 1S) and He(2 3S) metastable atoms

The velocity dependence of the title reactions was measured using crossed molecular beams and time-of-flight velocity dispersion of the metastable helium atoms. The relative collision energy ranged from 6–10 to 600–800 meV. The singlet cross section energy dependences are all of the ’’repulsive’’ type, i.e., increasing with energy at low energies, implying that the interaction potential well depths are ≲6–8 meV. The triplet cross sections are also generally repulsive, but the Ar, Kr, and O2 cases show evidence of minimums at the lowest energies. These observations are in qualitative agreement with the available interaction potential data. The cross section curves were put on an absolute basis by normalization to thermal quenching rate constants. The cross sections tend to approach the same magnitude at high energies and diverge at low energies. The singlet cross sections increase more rapidly than the triplet cross sections at low energies, with the singlet Ar, Kr, and N2 curves having especially steep slopes. Theoretical cross section curves were calculated for the He(1S,3S)/Ar, Kr cases using interaction potentials available from differential scattering studies. The results are in good agreement with experiment, and confirm the need for unusual low energy repulsive structure in the singlet potentials to explain the collisional energy dependence of chemi-ionization.

Primary photochemistry and photoisomerization of retinal at 77 degrees K in cattle and squid rhodopsins

The relative quantum yields of the photoreactions Rhodopsin in equilibrium Bathorhodopsin in equilibrium Isorhodopsin over an extended wavelength region have been determined in cattle and squid rhodopsins at 77 degrees K. The quantum yields were found to be wavelength independent and unchanged for samples suspended in D2O. The rhodopsin-bathorhodopsin forward and backward quantum yields sum to larger than one. These results are consistent with the previous suggestion that the excited singlet potential of rhodopsin has a single minimum along the 11-12 torsional coordinate. The values of the quantum yields are important for evaluating dynamic models of the rhodopsin-bathorhodopsin transition. We conclude that equilibration in the common excited state afer excitation of rhodopsin, as previously suggested, does not occur. Models involving molecular excitation trajectories conserving torsional momenta and excited state to ground state surface crossings better fit the data, and a semiquantitative analysis is presented. Probabilities of surface crossings are calculated.

A dilute hard-sphere bose-gas model calculation of low-density atomic hydrogen gas properties

The isolated pair wave equation is solved for two isolated hydrogen atoms interacting via the 3Σ u + potential, from which a scattering length a = 0.72 » is determined and used as an effective hard-core diameter in a dilute hard-sphere Bose-gas model calculation. In the low-density limit, these results for the ground state energy compare closely with earlier Monte Carlo data. Using established criteria for the values of density and temperature over which the hard-sphere model is valid, we have calculated the energy, first- and secondsound velocities, depletion factor, and superfluid transition temperature, and expressions are given for the specific heat and normal fluid fraction. The scattering length of atomic hydrogen interacting via the singlet potential is found to be 0.12 » and similar calculations for helium give a scattering length much too large to justify application of the hard-sphere model.

HNC neutron-matter calculations with the Paris potential

A formalism is developed for handling momentum-dependent potentials within the framework of hypernetted chain calculations of dense matter. Some new distribution functions are required and appropriate expressions are obtained for calculating them. The formalism is applied to neutron-matter calculations with the Paris potential. As a test, the first application is to the 1S 0 acting in all partial waves. A more realistic calculation which includes the singlet and triplet potentials in the isospin one channels was used to calculate the equation of state of dense neutron matter and to obtain neutron-star models. LOCV calculations were performed including all partial waves, but attempts to handle state dependence in the correlation function met with complications like those encountered with momentum independent potentials. Significant features of the results with the Paris potential are discussed.

A comparison of Mu-H and H-H electron spin exchange cross sections

The spin exchange cross sections for H-H and Mu-H collisions are calculated and compared. At low temperatures ( or approximately=400K), the thermally averaged cross sections are comparable and it is shown that the ratio of the Mu-H and H-H cross sections is given approximately by ( mu Mu-H/ mu H-H)1(p-1)/ where mu is the reduced mass and the difference between the triplet and singlet potentials is approximately proportional to r-p.

Penning ionisation of atomic hydrogen by metastable neon atoms

The author reports the energy spectrum of electrons which are emitted in Penning ionisation of atomic hydrogen by metastable neon atoms. The results suggest that the doublet interaction potential between Ne* and H is very similar to the ground-state singlet potential of NaH. The ionisation cross section for Ne*(3P0) is about five times larger than for Ne*(3P2).

Long-range helium excimer potentials (A,CΣu,g+1anda,cΣu,g+3) from high-resolution differential cross sections for He(2S1,2S3)+He

The long-range parts of the A,C /sup 1/..sigma../sup +//sub u/,g and a,c /sup 3/..sigma../sup +//sub u/,g excimer potentials of the He/sub 2/ molecule have been accurately determined from high-resolution differential-cross-section measurements in the relative kinetic-energy range from 18 to 140 meV. The barrier heights and internuclear distances of the intermediate maxima of the A and the a state have been obtained with an accuracy of better than 2--5 meV and 0.1 A, respectively. The long-range parts of the singlet potentials from the ab initio calculation by Gubermann and Goddard are always 5--20 meV higher than the potential determined from our experiments, but the splitting of the potentials coincides with our results within experimental accuracy for R > or = 3 A. The experimental setup, data evaluation, and the construction of the potential are described in detail. The complicated interference structure of the angular distribution is discussed with the help of the quantal deflection function. Total and excitation-transfer cross sections are calculated and compared to other experimental results, and the similarity to other exchange processes is pointed out.

A simple quantum chemical theory of dissociative adsorption

Potential energy curves for the adsorption of a hydrogen atom on the (100), (110), (111) and the stepped (311) crystal faces of copper have been calculated in the pairwise additive model for gas atom-solid interactions. A Morse function is used to represent the lowest singlet pairwise H-Cu interaction potential and its parameters are adjusted so that the calculated maximum bond energies conform with the available experimental data. Bond strength on the low index faces is found to increase with the adatom's local coordination number. Except for the edge sites, the steps on the (311) surface strengthen the bonds to sites on the component low index facets. A systematic study of the convergence of the bond energy as a function of the number of solid atoms is reported. The H-Cu(s) potential is shown to be relatively insensitive to changes in the first layer separation distance of the size inferred from experiment. A new model for diatom-solid potentials is proposed in which the diatom-solid potential is expressed as a sum of the differences between diatom-solid atom London-Eyring-Polanyi-Sato three-body potentials and the diatom singlet potential. This model is used to calculate potential curves for various approaches of a hydrogen molecule towards the same copper faces. H 2 is predicted to be physisorbed on each face. The atom-solid and diatom—solid potentials are used in conjunction with a model formulated by Lennard-Jones to estimate activation energies for dissociative adsorption. The correct order is obtained for the activation energies on the low index faces. Substantially lower activation energies are obtained for approaches toward many of the sites on the two low index facets of the (311) surface as compared to the same approaches towards the individual component faces. Dissociative adsorption is predicted to proceed without activation near the steps on this surface. In general, higher activation energies are obtained when the admolecule is perpendicular to the surface or facet in question. The simple idea that the activation energies are determined by small shifts of the atomic potential relative to the less structure-sensitive molecular potential works well for the low index faces, but is not wholly satisfactory for the stepped (311) surface. All results reported in this paper are negligibly different from those that are fully converged with respect to cluster size in the present model.

Accuracy of the unitary pole approximation at positive energies for local potentials containing a hard core

The accuracy of the unitary pole approximation (UPA) to the two-body $t$ matrix at positive energies has been examined for the case of a local potential with a hard core. To this effect the $S$-wave phase shifts and the half-shell functions (Baranger, Giraud, Mukhopadhyaya, and Sauer) have been calculated for the Herzfeld potential as well as for its UPA. The agreement between the two sets, though satisfactory, is not as good as reported by Levinger and O'Donoghue, who did similar calculations for various singlet potentials. This result may be attributed to the existence of a bound-state pole in $t$ matrix in the negative energy region in the case of the Herzfeld potential.NUCLEAR STRUCTURE Unitary pole approximation, hard core potential, positive energies.

“How can we determine the two-bodyt-matrix?”

We start with an assumed shape for the wavefunction of the ground state of the two-nucleon system. This wavefunction gives us the residue of thet-matrix at the bound-state pole-and using the unitary pole approximation (UPA) provides a good extrapolation procedure for other off-shell values of thet-matrix. (E. Harms has verified the accuracy of the UPA using the anti-bound state for theReid soft-core singlet potential.)

Accuracy of the unitary pole approximation for the reid triplet potential

The unitary pole approximation (UPA) has been shown to be quite accurate for a central attractive potential with a soft core, such as the Reid singlet potential. We examine its accuracy for the Reid triplet soft-core potential, which includes tensor and spin-orbit forces. We compare UPA values for the t-matrix t LL′ ( p, k; s) with Haftel's numerical values. Here L and L′ are angular momenta, either 0 or 2. The momenta are p and k, and we emphasize negative energy s. We find that the UPA fits Haftel's values for t 00 about as well as the UPA fits for the Reid singlet. The UPA is less successful for t 02 and t 22, but in general it fits Haftel's values better than does the Yamaguchi t-matrix.

Interaction of Two Metastable Triplet Helium Atoms

Ab initio quantum-mechanical calculations have been performed for the Σg+5, Σu+3, and Σg+1 states arising from the interaction of two 1s2s3S helium atoms. A rigorous upper bound to the quintet potential was found by use of the variational principle. Crude estimates of the autoionizing singlet and triplet states were obtained by the “stabilization” method. The quintet-state potentials exhibit a van der Waals minimum, and the triplet and singlet potentials exhibit more substantial minima. The behavior of the wavefunctions in the separated-atom limit was studied, and the range of applicability of the effective Heisenberg spin Hamiltonian was tested on the calculated potentials.

The singlet potential of alkali diatoms

The evaluation of alkali-alkali scattering experiments is facilitated if one considers spectroscopic knowledge. As an example, a “best” potential for the singlet ground state of NaCs is proposed.

Small angle scattering from crossed sodium and potassium beams

The small angle dependence of the differential cross-section for the elastic scattering of Na by K has been measured at relative velocities from 936 to 1420 m sec–1 using a crossed-beam technique. Quantum undulations in the cross-sections were observed at laboratory angles less than 2° and their origin is discussed. The positions of the observed peaks together with a singlet potential obtained from spectroscopic data yield information on the long-range dispersion forces and the triplet potential. For the triplet potential with an assumed Lennard-Jones 8 : 6 from the best agreement found between observation and forward calculation yielded ε= 2 × 10–14 ergs and rm= 5.6 Å, though the fit is not perfect.

Effect of the Baryon Excited States on theN−ΛandΛ−ΛForces

The $N\ensuremath{-}\ensuremath{\Lambda}$ and $\ensuremath{\Lambda}\ensuremath{-}\ensuremath{\Lambda}$ potentials caused by the exchange of two pions are calculated in the static theory, taking into account the resonance ${{Y}_{1}}^{*}$ in the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\Lambda}$ system and the (3-3) resonance in the $\ensuremath{\pi}\ensuremath{-}N$ system. The recoil of the baryons is included in an approximate way. It is shown that the presence of these resonances diminishes the spin-dependent part of the central potential and the tensor potential, and increases the spin-independent part of the central potential. The triplet potential turns out to be slightly stronger than the singlet potential at large distances, and slightly weaker than it closer in. If the resonances are omitted, the triplet potential is the stronger over the whole range. This last result is in mild disagreement with other work. Its relation to the choice of a one-channel or two-channel formalism is discussed.

Binding energies of light hyperfragments

The binding energies of ΛH 3 , ΛHe 4 and ΛH 4 , and ΛHe 5 are calculated using a independent pair approximation assuming the interactions are described by spin-dependent nucleon-nucleon and Λ-nucleon potentials with square-well shapes outside of hard cores. The calculated binding energies are presented as functions of the depths of the Λ-nucleon potentials for two possible ranges of these potentials. The experimental binding energies then determine the actual potential depths. The case that the singlet potential is stronger than the triplet potential is favoured for both ranges treated. This result leads to a prediction of zero spin for ΛHe 4 and ΛH 4 and no bound excited states for these four-particle hyperfragments. The two-particle Λ-nucleon system also turns out to be unbound.

Propriétés analytiques de la matrice S dans la diffusion par un potentiel, relativement à la force de ce potentiel

Analytical properties of the S matrix are obtained with respect to the strength of any potential in the radial Schrodinger equation. Some properties of the analogs of Regge trajectories are derived in the same way, which should give information on the radius of convergence of Born expansion. Enough information is obtained by restricting the study to potentials decreasing faster than an exponential at infinite range. Results are derived for the branches of the trajectories relative to anti-bound states. Restriction to superpositions of Yulkawa potentials gives information on some points. In the case of nucleon- nucleon scattering, strengihs of both singlet and triplet potentials belong to the same trajectory. As an example, they are calculated in the case of a Yukawa potential from the energies of the deuteron and of the antibound /sup 1/S/sub O/ state. (auth)

A separable potential for the two-nucleon ( T = 1) interaction

A separable potential in the isobaric state T = 1 is proposed on the basis of p—p scattering data up to about 100 MeV. The triplet part of this potential is taken to be purely of the spin-orbit type, with a range about half of that of the singlet potential. Potentials in states l ≧ 3 are neglected. It is found that such a potential can rather satisfactorily explain the angular shape of the unpolarized cross section as well as the magnitude of the polarization in scattering up to 100 MeV.