Four-Nucleon Scattering with a Correlated Gaussian Basis Method
Tóm tắt
Elastic-scattering phase shifts for four-nucleon systems are studied in an ab-initio type cluster model in order to clarify the role of the tensor force and to investigate cluster distortions in low energy d+d and t+p scattering. In the present method, the description of the cluster wave function is extended from (0s) harmonic-oscillator shell model to a few-body model with a realistic interaction, in which the wave functions of the subsystems are determined with the Stochastic Variational Method. In order to calculate the matrix elements of the four-body system, we have developed a Triple Global Vector Representation method for the correlated Gaussian basis functions. To compare effects of the cluster distortion with realistic and effective interactions, we employ the AV8′ potential + a three nucleon force as a realistic interaction and the Minnesota potential as an effective interaction. Especially for 1
S
0, the calculated phase shifts show that the t+p and h+n channels are strongly coupled to the d+d channel for the case of the realistic interaction. On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction. This difference between both potentials originates from the tensor term in the realistic interaction. Furthermore, the tensor interaction makes the energy splitting of the negative parity states of 4He consistent with experiments. No such splitting is however reproduced with the effective interaction.
Tài liệu tham khảo
Wildermuth K., Tang Y.C.: A unified theory of the nucleus. Vieweg, Braunschweig (1977)
Kamada H., Nogga A., Glöckle W., Hiyama E., Kamimura M. et al.: Benchmark test calculation of a four-nucleon bound state. Phys. Rev. C 64, 044001 (2001)
Varga K., Suzuki Y., Lovas R.G.: Microscopic multicluster description of neutron-halo nuclei with a stochastic variational method. Nucl. Phys. A 571, 447 (1997)
Varga K., Ohbayasi K., Suzuki Y.: Stochastic variational method with noncentral forces. Phys. Lett. B 396, 1 (1997)
Varga K., Usukura J., Suzuki Y.: Second bound state of the positronium molecule and biexcitons. Phys. Rev. Lett. 80, 1876 (1998)
Usukura J., Varga K., Suzuki Y.: Signature of the existence of the positronium molecule. Phys. Rev. A 58, 1918 (1998)
Suzuki Y., Varga K.: Stochastic variational approach to quantum-mechanical few-body problems. Lecture notes in physics. Springer, Berlin (1998)
Varga K., Suzuki Y.: Precise solution of few-body problems with the stochastic variational method on a correlated Gaussian basis. Phys. Rev. C 52, 2885 (1995)
Suzuki Y., Horiuchi W., Orabi M., Arai K.: Global-vector representation of the angular motion of few-particle systems II. Few-Body Syst. 42, 33 (2008)
Varga K., Suzuki Y., Usukura J.: Global-vector representation of the angular motion of few-particle systems. Few-Body Syst. 24, 81 (1998)
Carlson J., Schiavilla R.: Structure and dynamics of few-nucleon systems. Rev. Mod. Phys. 70, 743 (2008)
Pudliner B.S., Pandharipande V.R., Carlson J., Pieper S.C., Wiringa R.B.: Quantum Monte Carlo calculations of nuclei with A<7. Phys. Rev. C 56, 1720 (1997)
Navratil P., Kamuntavicius G.P., Barrett B.R.: Few-nucleon systems in a translationally invariant harmonic oscillator basis. Phys. Rev. C 61, 044001 (2000)
Viviani M.: Transformation coefficients of hyperspherical harmonic functions of an A-body system. Few-Body Syst. 25, 177 (1998)
Feldmeier H., Neff T., Roth R., Schnack J.: A unitary correlation operator method. Nucl. Phys. A 632, 61 (1998)
Neff T., Feldmeier H.: Tensor correlations in the unitary correlation operator method. Nucl. Phys. A 713, 311 (2003)
Arai K., Aoyama S., Suzuki Y.: Microscopic cluster model study of 3He+p scattering. Phys. Rev. C 81, 037301 (2010)
Phitzinger B., Hofmann M., Hale G.M.: Elastic p-3He and n-3H scattering with two- and three-body forces. Phys. Rev. C 64, 044003 (2001)
Deltuva A., Fonseca A.C.: Four-nucleon scattering: Ab initio calculations in momentum space. Phys. Rev. C 75, 014005 (2007)
Deltuva A., Fonseca A.C.: Four-body calculation of proton-3He scattering. Phys. Rev. Lett 98, 162502 (2007)
Quaglioni S., Navratil P.: Ab initio many-body calculations of nucleon-nucleus scattering. Phys. Rev. C 79, 044606 (2009)
Quaglioni S., Navratil P.: Ab initio many-body calculations of n-3H, n-4He, p-3,4He, and n-10Be scattering. Phys. Rev. Lett. 08, 092501 (2008)
Viviani M., Rosati S., Kievsky A.: Neutron-3H and proton-3He zero energy scattering. Phys. Rev. Lett. 81, 1580 (1998)
Viviani M., Kievsky A., Rosati S., George E.A., Knulson L.D.: The A y problem for p-3He elastic scattering. Phys. Rev. Lett. 86, 3739 (2001)
Viviani M., Kievsky A., Girlanda L., Marcucci L.E., Rosati S.: Neutron-triton elastic scattering. Few-Body Syst. 45, 119 (2009)
Lazauskas R., Carbonell J., Fonseca A.C., Viviani M., Kievsky A., Rosati S.: Low energy n-3H scattering: a novel testground for nuclear interactions. Phys. Rev. C 71, 034004 (2005)
Fisher B.M. et al.: Proton-3He elastic scattering at low energies. Phys. Rev. C 74, 034001 (2006)
Arriaga A., Pandharipande V.R., Schiavilla R.: Variational Monte Carlo calculations of the 2H(d, γ)4He reaction at low energies. Phys. Rev. C 43, 983 (1991)
Sabourov K. et al.: Experimental and theoretical study of the 2H(d, γ)4He reaction below E c.m.=60 keV. Phys. Rev. C 70, 064601 (2004)
Hofmann H.M., Hale G.M.: 4He experiments can serve as a database for determining the three-nucleon force. Phys. Rev. C 77, 044002 (2008)
Hofmann H.M., Hale G.M.: Microscopic calculation of the 4He system. Nucl. Phys. A 613, 69 (1997)
Hofmann H.M., Hale G.M.: Microscopic calculation of the spin-dependent neutron scattering lengths on 3He. Phys. Rev. C 68, 021002 (2003)
Deltuva A., Fonseca A.C.: Ab initio four-body calculation of n-3He, p-3H, and d-d scattering. Phys. Rev. C 76, 021001 (2007)
Deltuva A., Fonseca A.C., Sauer P.U.: Four-nucleon system with Δ-isobar excitation. Phys. Lett. B 660, 471 (2008)
Lazauskas R., Carbonell J.: Ab-initio calculations of four-nucleon elastic scattering. Few-Body Syst. 34, 105 (2004)
Ciesielski F., Carbonell J., Gignoux C.: Low energy n + t scattering and the NN forces. Phys. Lett. B 447, 199 (1999)
Assenbaum H.J., Langanke K.: Low-energy 2H(d,γ)4He reaction and the D-state admixture in the 4He ground state. Phys. Rev. C 36, 17 (1987)
Fowler W.A., Caughlan G.R., Zimmerman B.A.: Thermonuclear reaction rates. Annu. Rev. Astron. Astrophys. 5, 525 (1967)
Baye D., Heenen P.H., Libert-Heinemann M.: Microscopic R-matrix theory in a generator coordinate basis: (III). Multi-channel scattering. Nucl. Phys. A 291, 230 (1977)
Kanada H., Kaneko T., Saito S., Tang Y.C.: Microscopic study of the d+α scattering system with the multi-channel resonating-group method. Nucl. Phys. A 444, 209 (1985)
Arai K., Descouvemont P., Baye D.: Low-energy 6He+p reactions in a microscopic multicluster model. Phys. Rev. C 63, 044611 (2001)
Descouvemont P., Baye D.: The R-matrix theory. Rep. Prog. Phys. 73, 036301 (2010)
Navratil P., Quaglioni S.: Ab initio many-body calculations of deuteron-4He scattering and 6Li states. Phys. Rev. C 83, 044609 (2011)
Pudliner B.S., Pandharipande V.R., Carlson J., Pieper S.C., Wiringa R.B.: Quantum Monte Carlo calculations of nuclei with A≤7. Phys. Rev. C 56, 1720 (1997)
Hiyama E., Gibson B.F., Kamimura M.: Four-body calculation of the first excited state of 4He using a realistic NN interaction: 4 He(e, e′)4He(0+ 2) and the monopole sum rule. Phys. Rev. C 70, 031001 (2003)
Thompson D.R., LeMere M., Tang Y.C.: Systematic investigation of scattering problems with the resonating-group method. Nucl. Phys. A 286, 53 (1977)
Boys S.F.: The integral formulae for the variational solution of the molecular many-electron wave equations in terms of Gaussian functions with direct electronic correlation. Proc. R. Soc. London. Ser. A 258, 402 (1960)
Singer K.: The use of Gaussian (exponential quadratic) wave functions in molecular problems. I. General formulae for the evaluation of integrals. ibid. 258, 412 (1960)
Suzuki Y., Usukura J.: Excited states of the positronium molecule. Nucl. Inst. Method B 171, 67 (2000)
Suzuki Y., Usukura J., Varga K.: New description of orbital motion with arbitrary angular momenta. J. Phys. B 31, 31 (1998)
Horiuchi W., Suzuki Y.: Inversion doublets of 3N+N cluster structure in excited states of 4He. Phys. Rev. C 78, 034305 (2008)
Tilley D.R., Weller H.R., Hale G.M.: Energy levels of light nuclei A=4. Nucl. Phys. A 541, 1 (1992)
Tamagaki R.: Potential models of nuclear forces at small distances. Prog. Theor. Phys. 39, 91 (1968)
Santos F.D., Arriaga A., Eiró A.M., Tostevin J.A.: 4He D-state effect in the d(d, γ)4He reaction. Phys. Rev. C 31, 707 (1985)
Wachter B., Mertelmeier T., Hofmann H.M.: The 2H(d, γ)4He reaction and the D-state of the alpha particle: a microscopic study. Phys. Lett. B 200, 246 (1988)
Angulo C., Arnould M., Rayet M., Descouvemont P., Baye D. et al.: A compilation of charged-particle induced thermonuclear reaction rates. Nucl. Phys. A 656, 3 (1999)