×

Hartree-Fock theory in nuclear physics. (English) Zbl 0607.35078

We present the Hartree-Fock approximation method for the many-body problems in Quantum Mechanics corresponding to the interaction of neutrons and protons. We study the various forms of Hartree-Fock equations, the questions related to spin-dependence and spin-orbit forces, symmetries of the nucleus and symmetry breakings and time- dependent Hartree-Fock equations.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
81V05 Strong interaction, including quantum chromodynamics
35J60 Nonlinear elliptic equations
81R40 Symmetry breaking in quantum theory
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] J. F. G. AUCHMUTY and R. BEALS, Arch. Rat. Mech. Anal, 65 (1977), pp. 249-261. Zbl0366.76083 MR446076 · Zbl 0366.76083 · doi:10.1007/BF00280443
[2] J. F. G. AUCHMUTY and R. BEALS, Astrophys J., 165 (1971), pp. 79-82.
[3] J. B. BARDEEN, L. N. COOPER and J. R. SCHRIEFFER, Phys. Rev., 10P (1957), p. 1175. Zbl0090.45401 · Zbl 0090.45401 · doi:10.1103/PhysRev.108.1175
[4] B. BAUMGARTNER, Comm. Math. Phys., 47 (1976), pp. 215-219. MR406156
[5] H. BERESTYCKI and P. L. LIONS, Arch. Rat. Mech. Anal., 82 (1983), pp. 313-346, and pp. 347-375. Zbl0556.35046 MR695536 · Zbl 0556.35046
[6] J. F. BERGER, M. GIROD and D. GOGNY, Nucl. Phys. A. , 428 (1984), pp. 236-296.
[7] H. BETHE, Ann. Rev. Nucl. Sci., 11 (1971), pp. 93-244.
[8] H. BETHE, Phys. Rev. , 167 (1968), p. 879.
[9] C. BLOCH and A. MESSIAH, Nucl. Phys., 39 (1962), p. 95. Zbl0127.45701 MR145923 · Zbl 0127.45701 · doi:10.1016/0029-5582(62)90377-2
[10] N. N. BOGOLYUBOV, Sov. Phys. JETP, 7 (1958), p 41 , Sov. Phys. Usp., 2 (1959), p. 236., Usp. Fiz. Nauk. 67 (1959), p. 549.
[11] A. BOHR, Mat. Fys. Medd. Dan. Vid. Setsh., 26 (1952).
[12] T. CAZENAVE and P. L. LIONS, Comm. Math. Phys., 85 (1982), pp. 549-561. Zbl0513.35007 MR677997 · Zbl 0513.35007 · doi:10.1007/BF01403504
[13] C. V. COFFMAN, Arch. Rat. Mech. Anal., 46 (1972), pp. 81-95. Zbl0249.35029 MR333489 · Zbl 0249.35029 · doi:10.1007/BF00250684
[14] J. DECHARGÉ and D. GOGNY, Phys. Rev. C., 21 (1980), pp. 1568-1593.
[15] M. EFFER, Cours à l’IN2 P3, École Juliot Curie de Physique Nucleaire, 1983.
[16] H. FLOCARD, Nukleonika, 24 (1979), pp. 19-66.
[17] V. FOCK, Z. Phys., 61 (1930), pp. 126-148. JFM56.1313.08 · JFM 56.1313.08
[18] J. GINIBRE and G. VELO, J. Funct. Anal., 32 (1979), pp. 1-72, Ann. I. H. P. A. 28 (1978), pp. 287-316. MR533219
[19] J. GINIBRE and G. VELO, Mat. Zeit., C. R. Acad. Sci. Paris 288 (1979), pp. 683-686. Zbl0397.35013 MR533902 · Zbl 0397.35013
[20] J. GINIBRE and G. VELO. Ann. I. H. P. Anal. Non. Lin. (1985).
[21] M. GIROD and B. GRAMMATICOS, Phys. Rev. C., 27 (1981), p. 2317.
[22] J. GOLDSTONE, Nuov. Cim., 19 (1961), p. 154. Zbl0099.23006 MR128374 · Zbl 0099.23006 · doi:10.1007/BF02812722
[23] D. HARTREE, Proc. Cambridge Philos. Soc., 24 (1928), pp. 89-132.
[24] P. W. HIGGS, Phys. Lett., 12 (1964), p. 132.
[25] K. KUMAR, Ch. LAGRANGE and M. GIROD, Phys. Rev. C. 3, 31 (1985), p. 762.
[26] E. H. LIEB, Phys. Rev. Lett. 46 (1981), pp. 457-459 and 47 (1981), p.68. MR601336
[27] E. H. LIEB, Rev. Mod. Phys., 53 (1981), pp. 603-641. Zbl1114.81336 · Zbl 1114.81336 · doi:10.1103/RevModPhys.53.603
[28] E. H. LIEB, Studies in Appl. Math., 57 (1977), pp. 93-105. Zbl0369.35022 MR471785 · Zbl 0369.35022
[29] E. H. LIEB, In Proc. Int. Cong. Math. Vancouver, 1974, pp. 383-386.
[30] E. H. LIEB and B. SIMON, Comm. Math. Phys., 53 (1977), pp. 185-194. MR452286
[31] E. H. LIEB and B. SIMON, Adv. Math., 23 (1977), pp. 22-116. Zbl0938.81568 MR428944 · Zbl 0938.81568 · doi:10.1016/0001-8708(77)90108-6
[32] P. L. LIONS, C. R. Acad Sci Paris, 294 (1982), pp. 377-379. Zbl0488.35072 MR658560 · Zbl 0488.35072
[33] P. L. LIONS, Ann. I. H. P. Anal. Nonlin, 1 (1984), pp. 109-135 and pp. 223-283. C. R. Acad. Sci. Paris, 294 (1982), pp. 261-264. MR778974
[34] P. L. LIONS Riv. Math. Iberoamericana, 1 (1985), pp. 145-201 and pp. 45-121, C. R. Acad. Sci. Paris, 296 (1983), pp. 645-648.
[35] P. L. LIONS, In < Nonlinear Variational problems>, Pitman, London, 1985. MR807536
[36] P. L. LIONS, J. Funct. Anal. 41 (1981), pp. 236-275. Zbl0464.49019 MR615163 · Zbl 0464.49019 · doi:10.1016/0022-1236(81)90089-6
[37] P. L. LIONS, J. Funct. Anal., 49 (1982), pp. 315-334. Zbl0501.46032 MR683027 · Zbl 0501.46032 · doi:10.1016/0022-1236(82)90072-6
[38] P. L. LIONS, Nonlinear Anal. T. M. A., 5 (1981), pp. 1245-1256. Zbl0472.35074 MR636734 · Zbl 0472.35074 · doi:10.1016/0362-546X(81)90016-X
[39] P. L. LIONS, In Nonlinear Problems Present and Future, Eds A. Bishop, D. Campell, B. Nicolaenko, North-Holland, Amsterdam, 1983. MR675623
[40] P. L. LIONS, Nonlinear Anal T. M. A., 4 (1980), pp. 1063-1073. Zbl0453.47042 MR591299 · Zbl 0453.47042 · doi:10.1016/0362-546X(80)90016-4
[41] J. W. NEGELE, Physics To Day (1985).
[42] J. W. NEGELE, Rev Modern Phys., 54 (1982), pp. 913-1015.
[43] J. W. NEGELE, Phys Rev. C 1, 4 (1970), p. 1260.
[44] P. QUENTIN and H. FLOCARD, Ann. Rev. Nucl. Part. Sci., 28 (1978), pp. 523-596.
[45] J. C. SLATER, Phys. Rec., 81 (1951), pp. 385-390. Zbl0042.23202 · Zbl 0042.23202 · doi:10.1103/PhysRev.81.385
[46] W. STRAUSS, Comm. Math. Phys., 55 (1977), pp. 149-162. Zbl0356.35028 MR454365 · Zbl 0356.35028 · doi:10.1007/BF01626517
[47] J. G. VALATIN, Phys. Rev., 122 (1961), p. 1012. Zbl0097.43603 MR121197 · Zbl 0097.43603 · doi:10.1103/PhysRev.122.1012
[48] D. VAUTHERIN and D. M. BRINK, Phys. Rev. C., 9 (1972), p. 626-647.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.