One-channel Approximation Research Articles

Nucleon- J/ψ and nucleon- ηc scattering in Pc pentaquark channels from lattice QCD

The lattice QCD simulation of $NJ/\psi$ and $N\eta_c$ scattering is performed at $m_\pi\simeq 266~$MeV in channels with all possible $J^P$. This includes $J^P=3/2^\pm$ and $5/2^\pm$ where LHCb discovered $P_c(4380)$ and $P_c(4450)$ pentaquark states in proton$-J/\psi$ decay. This is the first lattice simulation that reaches the energies 4.3-4.5 GeV where pentaquarks reside. Several decay channels are open in this energy region and we explore the fate of $P_c$ in the one-channel approximation in this work. Energies of eigenstates are extracted for the nucleon-charmonium system at zero total momentum for all quantum numbers, i.e. six lattice irreducible representations. No significant energy shifts are observed. The number of the observed lattice eigenstates agrees with the number expected for non-interacting charmonium and nucleon. Thus, we do not find any strong indication for a resonance or a bound state in these exotic channels within one-channel approximation. This possibly indicates that the coupling of $NJ/\psi $ channel with other two-hadron channels might be responsible for $P_c$ resonances in experiment. One of the challenges of this study is that up to six degenerate $J/\psi(p) N(-p)$ eigenstates are expected in the non-interacting limit due non-zero spins of $J/\psi$ and N, and we establish all of them in the spectra.

Examples of a semiempirical design of nucleation rate surfaces for systems with monotropic polymorphous phase transitions

Examples of the topology of nucleation rate surfaces for systems with monotropic polymorphic transitions constructed using a new concept for the semiempirical design of such surfaces over p-T phase equilibrium diagrams, where p is pressure and T is temperature, are presented. It is shown in these cases that multichannel nucleation corresponding to a set of independent nucleation rate surfaces occurs. Previous attempts to describe such systems in the one-channel approximation of the theory are not valid. We conclude that the obtained topologies of nucleation surfaces can be used as examples that illustrate the generalized rule of the sequence of phases, the first version of which was formulated by Ostwald.

AComparative Study of Approximate Treatments of the Density Polarization in CN-

The simple perturbative description of the main polarization effects in molecular systems is tested and calibrated using the modified Hamiltonian MNDO SCF results for the cyano group CN- perturbed by positive or negative point charges. The relative importance of various polarization channels is examined and the reliability of the MNDO predictions is investigated by testing them against the respective ab initio modified Hamiltonian results. It is shown that the δ-function approximation of the point-charge perturbative potential leads to semiquantitatively correct density relaxation patterns, already within one-channel approximation.

R-matrix analysis of the beta +/--delayed alpha spectra from the decay of 8Li and 8B.

The general question of the analysis of beta-delayed particle emission is discussed. It is emphasized that neither an integrated Fermi function nor a beta branching ratio is, in general, rigorously defined for beta decay to a specific level (resonance). As an example, spectra of breakup \ensuremath{\alpha} particles observed following $^{8}\mathrm{Li}$(${\ensuremath{\beta}}^{\mathrm{\ensuremath{-}}}$${)}^{8}$Be and $^{8}\mathrm{B}$(${\ensuremath{\beta}}^{+}$${)}^{8}$Be are analyzed by the many-level one-channel approximation of R-matrix theory. In addition, the L=2 \ensuremath{\alpha}-\ensuremath{\alpha} elastic scattering phase shifts are analyzed up to ${E}_{\ensuremath{\alpha}}$=34 MeV. It is found that satisfactory fits are obtained without introducing intruder states below 26-MeV excitation. Gamow-Teller matrix elements are extracted for decay to the 3.0-MeV first-excited state of $^{8}\mathrm{Be}$ and for the doublet near 16 MeV. The width and location of the $^{8}\mathrm{Be}$ 3.0-MeV state are also obtained. The results are compared to shell-model predictions.

Multiple-ionization satellites in LII,III X-ray emission of elements of period four in compounds

A study has been made of the influence of multiple-ionization satellites on the form of LII,III in emission spectra of elements of the beginning of period four in compounds. In order to simulate the influence of the environment on the intensity of the satellite radiation in KCl and Sc2O3, the calculation was carried out in KH6 and ScH6 clusters. A one-channel approximation of the one-center method was used to calculate the one-electron orbitals of the clusters. It was found that the polarization of the functions of valence electrons during the appearance of an additional vacancy in the 3p shell the almost-tenfold increase in the lifetime of the 2p−13p−1 configuration relative to the 2p−1 configuration leads to an appreciable influence of the multiple-ionization satellites on the LIII,III emission spectrum of potassium. In the case of scandium, the effect is slightly smaller because of the appearance of valent states located in the region of the central atom (which leads to a decrease in the lifetime of the 2p−13p−1 configuration), a decrease in the probability of emission of a 3p electron, and a reduction of the polarization of valent electrons upon the appearance of a 3p vacancy.

Resonating-group study and importance of exchange effects in the α + 6Li system

The resonating-group method in the one-channel approximation is used to investigate the α + 6Li system. The result shows that, especially at relatively high energies, reasonable agreement with experiment can be obtained. In particular, the cross-section rise in the backward angular region is well accounted for. The effects of internuclear antisymmetrization, represented by various nucleon-exchange terms in the kernel function, have also been carefully examined. Here some of the interesting findings are that the blocking effect is quite significant in this system and the two-exchange terms (sometimes even the three-exchange terms) seem to have only minor influence on the scattering cross section.

The use of second order potentials in the theory of scattering of charged particles by atoms. VII. The partial wave formalism and elastic scattering of electrons by hydrogen and helium

The second order potential approximation of Bransden and Coleman (1972) is applied in a partial wave formalism to the elastic scattering of electrons from hydrogen and helium atoms. Differential, integrated, and total cross sections are presented for hydrogen in the energy range 100-200 eV and for helium in the range 50-500 eV. A one-channel approximation is used and the effect of exchange is included to first order in the potential. Conclusions are drawn as to the validity of the impact parameter approximation used in previous applications of the method.

On the Inner Repulsive Effect Due to the Pauli Principle between Nuclear Composite Particles

The effect of the Pauli exclusion principle in the short range· part of interactions between nuclear composite particles is investigated in the case that there are some relative which are not exactly forbidden but forbidden. These almost forbidden states (AFS) are coupled only weakly t~ the incoming relative states. Thus, the relative wave function is required to be approximately orthogonal to these AFS which are located in the inner region between composite particles. This gives rise to a strong repulsive effect characterized by the energy-independent inner nodal behavior as observed in the case of a-a scattering. However, at the energies characteristic of the.AFS, the coupling to the AFS from the incident wave becomes very effective, and resonance-like contributions are brought about within the one-channel approximation. With respect to this feature, the Levinson theorem is discussed. § I. Introduction The effect of the Pauli· principle is remarkably important in interactions between nuclear composite particles. The interaction between a-particles pro­ vides us with a typical .example. The experimental phase shifts in a-a scattering are well reproduced by an energy-independent local potential at low and inter­ mediate energies?J, 2l As striking features of such a phenomenological potential, the inclusion of a strong repulsive core with a radius of about 2 fm is required for the relative s and d states·, and the attractive part outside the core is system­ atically dependent on the angular-momentum (l). By calculations with the re­ sonating group method applied· to a-a scattering,8l it has been shown that the eff·ect of the nonlocality originating from the antisymmetrization is completely responsible for the above features of the a-a phenomenological potential. The presence· of the repulsive core can be understood as a result of· the energy-independent inner nodal behavior of the a-a relative wave function,'h 6) since the outermost nodal point coincides well with the radius of the repulsive core in a wide region of energies. It should be noted ·that the inner nodal bee havior is not due to the -existence of any bound states. 6 l A simple picture comprising such important aspects obtained by the res

Evidence for neutron exchange in the 3He 4He elastic scattering at medium energies

The differential cross section was measured for 66 to 103 MeV 4He elastic scattering on 3He ( E CM = 28 t0 44 MeV). The experimental values are compared with results of cluster model calculations in the one-channel approximation. Theoretical and experimental results agree qualitatively with respect to angular and energy dependence. The observed backward peaking is attributed to neutron exchange which is practically independent of spin-orbit effects.

Study of N + α system with the resonating-group method

Abstract The n + α and p + α systems are considered with the resonating-group method in the onechannel approximation. The nucleon-nucleon potential used has both a central part and a spinorbit component. From the results it is found that very good agreement with experiment can be obtained in the energy region below the reaction thresholds. In fact, even above the reaction thresholds where the one-channel approximation is expected to be less valid, the results are quite satisfactory. An effective potential between the clusters is also constructed. From this potential it is determined that the requirement of antisymmetry for the total wave function is very important. In particular, it creates an odd-even feature, wherein the effective central and the effective one-body spin-orbit potentials in the odd-l states are appreciably different from those in the even-l states.

Elastic Scattering ofHe3byHe4from 17.8 to 30.0 MeV

Differential cross sections for the elastic scattering of ${\mathrm{He}}^{3}$ by ${\mathrm{He}}^{4}$ have been measured from 21.9 to 155.0\ifmmode^\circ\else\textdegree\fi{} (c.m.) at ${\mathrm{He}}^{3}$ energies of 17.79, 19.99, 22.00, 23.98, 26.00, 28.00, and 30.00 MeV (lab). The relative standard deviations of the data are typically less than 2.5%, but become larger at angles where the cross section is very low. In addition to relative errors, the over-all error includes a standard deviation of 3% in the cross-section scale. The measurements are compared with theoretical calculations using the resonating-group method in the one-channel approximation. Differences between theory and experiment can be qualitatively understood as being caused mainly by the omission of reaction channels in the theory.

Study ofHe3+He3Elastic Scattering and the NucleusBe6

Differential cross sections for ${\mathrm{He}}^{3}$ + ${\mathrm{He}}^{3}$ elastic scattering have been measured at 18 angles from 12.5 to 45\ifmmode^\circ\else\textdegree\fi{} (lab) at energies of 17.91, 20.00, 22.00, 24.00, 26.00, 28.00, and 30.00 MeV (lab). In addition, differential cross sections have been measured at intermediate energies from 19.00 to 32.00 MeV (lab) at angles of 20, 28, 36, and 45\ifmmode^\circ\else\textdegree\fi{} (lab). The relative standard deviations of the data are generally less than 2%, and there is an additional standard deviation in the cross-section scale of 3%. The measurements are compared with theoretical calculations using the resonating-group method in the one-channel approximation. A broad resonance in the $l=3$ partial wave is predicted by the theory, and such a resonance has been observed in the present experiment. Differences between theory and experiment can be qualitatively understood as being caused principally by omission in the theory of reaction channels and noncentral forces. The effect of radial distortion in resonating-group calculations for the ${\mathrm{He}}^{3}$ + ${\mathrm{He}}^{3}$ system has also been investigated in an approximate manner. It is found that the effect can be quite significant for calculations of the energies of states in ${\mathrm{Be}}^{6}$ below the ${\mathrm{He}}^{3}$ + ${\mathrm{He}}^{3}$ threshold.

Study of the d + d system using the method of resonating-group structure

The method of resonating-group structure with a one-channel approximation is used to study the d + d and d ∗ + d ∗ systems. The calculated 2H(d, d) 2H differential cross sections agree fairly well with those determined experimentally. Also, evidence is found for an l = 1 state near the d + d threshold and possibly, a D-wave resonance near 30 MeV excitation in 4He. Further, no indication of the existence of a bound 4n system is obtained.

Further study of α + α scattering

The α + α scattering problem is investigated with the resonating-group method in the one-channel approximation, using an improved nucleon-nueleon potential. The results are significantly better than those obtained in previous α + α calculations using this method.

Correction to the potential in born approximation arising from direct-channel strips.—II

The ππ partial wave ampltude (p.w.a.) is studied in the one-channel approximation for the statel=I=1. The Born approximation to the force operating in the direct channel is assumed to be saturated by σ-exchange in the crossed reactions for this state. This amounts to a “strip approximation” to the force. However, the direct channel strips must also contribute to the potential and there are 2 relatively simple ways to estimate this effect. The first was treated in a previous paper and involved putting an asymptotic constraint on the p.w.a.,B 1 (ν) =A 1 (ν)/ν l which has the threshold factor divided out. The correction to the Born approximation was an attractive force in the statel=I=1. The second method is the subject of this paper and involves working with the p.w.a.,A 1 l (ν), and imposing on it the usual threshold constraint. The correction to the Born approximation in this case is a strong repulsive force. The 2 methods give qualitatively very different effects in ππ scattering, although the present method is probably more reliable. We finally show how to relate the 2 corrections at low energies.

Phase shifts of d> + α scattering

The resonating-group method with an one-channel approximation is used to study the d + α elastic scattering problem. The result shows that, in the excitation region below 10 MeV, there is no excited odd-parity P level in 6Li which has predominantly a d + α cluster structure.

Study of 3H+ 3H, 3H+ 3He, and 3He+ 3He systems with the resonating-group method

The 3He+ 3He, 3H+ 3H, and 3He+ 3H systems are examined using the resonating-group method with a one-channel approximation. A two-body central potential which fits the low-energy nucleon-nucleon scattering data is used. The radii of the clusters are fixed according to experimental data. The result shows that the agreement between the calculated and experimental differential cross sections is good for the 3He+ 3He and 3H+ 3H systems but is only fair for the 3He+ 3H system. The calculated phase shifts are analysed with a one-level formula, and a number of P- and F-resonant levels in the compound nuclei 6He, 6Li and 6Be are found. The question about the existence of excited states below the 3He+ 3He, 3H+ 3H and 3He+ 3H thresholds has also been examined. Here, the result shows that many S- and D-levels do exist in these energy regions.

Resonating-Group Calculation ofHe3-He3Scattering

The ${\mathrm{He}}^{3}$-${\mathrm{He}}^{3}$ elastic scattering is considered in the c.m. energy range of 0-20 MeV using the resonating group method in the one-channel approximation. A two-body central potential of Gaussian form which fits the low-energy nucleon-nucleon scattering data as well as possible is used. The saturation character which is not contained in this potential is approximately taken into account by fixing the radii of the clusters according to experimental data. Phase shifts up to $l=6$ are calculated, and a rather broad $l=3$ resonant level in ${\mathrm{Be}}^{6}$ with an excitation energy of about 25 MeV is predicted. Angular distributions are calculated at ten energies. The agreement with experimental data in the range 1.5 to 6.0 MeV is excellent, while that with the data from 6.0 to 12.0 MeV is somewhat worse, but still satisfactory. An optical-model analysis is also performed at an energy of 12 MeV and a reaction cross section of about 450 mb is predicted. This indicates that, at higher energies, channels other than the ${\mathrm{He}}^{3}$-${\mathrm{He}}^{3}$ channel should be included in the resonating-group calculation to achieve a better agreement with experiment.

Low-Energyπ−ΛInteraction, and theΣΛπCoupling Constant

A semiphenomenological study of the dynamics of the first hyperon resonance ${{Y}_{1}}^{*} (1385)$ has been made in a one-channel approximation by the techniques of partial-wave dispersion relations. Contributions from $\ensuremath{\Sigma}$ and ${{Y}_{1}}^{*}$ exchange, and the exchange of a low-energy $s$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ pair, to dispersion relations for the ${P}_{\frac{3}{2}}$ $\ensuremath{\pi}\ensuremath{-}\ensuremath{\Lambda}$ scattering amplitude were evaluated on the physical and crossed physical cuts. The coupling constant $g\ensuremath{\Sigma}\ensuremath{\Lambda}\ensuremath{\pi}$ and a parameter related to the ${P}_{\frac{3}{2}}\ensuremath{\pi}\ensuremath{-}\ensuremath{\Lambda}$ scattering length were varied so that the amplitude calculated from the dispersion relation was consistent with the input resonant amplitude on both cuts simultaneously. This could be achieved for $g\ensuremath{\Sigma}\ensuremath{\Lambda}{\ensuremath{\pi}}^{2}=10.9\ifmmode\pm\else\textpm\fi{}0.3$ The dynamics of ${{Y}_{1}}^{*}$ are found to depend almost as much on the exchange of the $s$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ pair as on $\ensuremath{\Sigma}$ exchange.

Elastic scattering of slow electrons by helium

Phase shifts for elastic collisions between electrons and helium atoms are calculated for l=0, 1 and 2 by numerical integration of the scattering equation in a one-channel approximation. When a polarization potential is included the zero energy cross section is found to be 16.50 a02.