Spectroscopy in the Nuclear <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mrow><msub><mrow><mi>f</mi></mrow><mrow><mfrac><mrow><mn>7</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></mrow></math></span> Shell

J. D. McCullen; B. F. Bayman; Larry Zamick

doi:10.1103/PhysRev.134.B515

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Spectroscopy in the Nuclear $1 f_{\frac{7}{2}}$ Shell

J. D. McCullen, B. F. Bayman, and Larry Zamick

Palmer Physical Laboratory, Princeton University, Princeton, New Jersey

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Phys. Rev. 134, B515 – Published 11 May, 1964

DOI: https://doi.org/10.1103/PhysRev.134.B515

Abstract

The intent of the work reported here has been to ascertain which properties of nuclei with $20 \leq Z$ , $N \leq 28$ are consistent with wave functions composed of a ${Ca}^{40}$ core plus $Z - 20$ protons and $N - 20$ neutrons in the $1 f_{\frac{7}{2}}$ shell. We have attempted to determine the $1 f_{\frac{7}{2}}$ nucleon-nucleon interaction from the observed levels of ${Sc}^{42}$ , assuming that these can be interpreted as due to the configuration ${(1 f_{\frac{7}{2}})}^{2}$ . Following Talmi, we have then treated this interaction exactly, within the framework of our pure configuration assumption. We have found that many of the observed properties of these nuclei are reproduced by this model, in particular the systematics of low-lying nuclear spins, magnetic moments, $ft$ values, and ( $p, d$ ) and ( $d, p$ ) spectroscopic factors. However, several nuclei have more low-lying states than the ${(1 f_{\frac{7}{2}})}^{n}$ configuration can provide at the corresponding energies.

References (46)

R. D. Lawson and J. L. Uretsky, Phys. Rev. 106, 1369 (1957) I. Talmi, in Proceedings of the Rehovoth Conference on Nuclear Structure (North-Holland Publishing Company, Amsterdam, 1958)
I. Talmi and I. Unna, Ann. Rev. Nucl. Sci. 10, 353 (1960)
I. Talmi, Rev. Mod. Phys. 34, 704 (1962)
A. de-Shalit and I. Talmi, Nuclear Shell Theory (Academic Press Inc., New York, 1963)
H. A. Jahn, Proc. Roy. Soc. (London) A205, 192 (1951)
S. P. Pandya, Phys. Rev. 103, 956 (1956) S. Goldstein and I. Talmi, 102, 598 (1956)
R. H. Bassel, R. M. Drisko, and G. R. Satchler, Oak Ridge National Laboratory Technical Report ORNL-3240, 1962 (unpublished)
W. Tobocman, Theory of Direct Nuclear Reactions (Oxford University Press, London, 1961)
P. C. Rogers and G. E. Gordon, Phys. Rev. 129, 2653 (1963)
N. Sarma (private communication)
I. Talmi, Phys. Rev. 126, 1096 (1962)
K. Way et al. in Landolt-Bornstein, New Series, Energy Levels of Nuclei, edited by A. M. Hellwege and K. H. Hellwege (Springer-Verlag, Berlin, 1961), Vol. 1
H. W. Kendall and I. Talmi, Phys. Rev. 128, 792 (1962) J. Vervier, Phys. Letters 5, 79 (1963) J. E. Schwager, Phys. Rev. 121, 569 (1961) [27]
G. Bassani, L. Colli, E. Gadioli, and I. Iori, Nucl. Phys. 36, 471 (1962)
R. R. Wilson, A. A. Bartlett, J. J. Kraushaar, J. D. McCullen, and R. A. Ristinen, Phys. Rev. 125, 1655 (1962) L. T. Dillman, J. J. Kraushaar, and J. D. McCullen, Nucl. Phys. 42, 383 (1963)
H. O. Funsten, N. R. Roberson, and E. Rost (to be published) B. F. Bayman, H. O. Funsten, N. R. Roberson, E. Rost, and R. Sherr, preliminary report by R. Sherr in Proceedings of The Padua Conference on Direct Interactions and Nuclear Reaction Mechanisms (Gordon and Breach, New York, 1963)
T. Komoda (to be published)
G. J. McCallum, A. T. G. Ferguson, and G. S. Mani, Nucl. Phys. 17, 116 (1960) N. O. Lassen and C. Larsen, 43, 183 (1963)
J. L. Yntema (private communication)
R. W. Bauer, J. D. Anderson, and L. J. Chrittensen, Phys. Rev. 130, 312 (1963)
M. H. Macfarlane, B. J. Raz, J. L. Yntema, and B. Zeidman, Phys. Rev. 127, 204 (1962)
P. C. Simms, N. Benczer-Koller, and C. S. Wu, Phys. Rev. 121, 1169 (1961)
L. H. Th. Rietjens, O. M. Bilaniuk, and M. H. Macfarlane, Phys. Rev. 120, 527 (1960) J. L. Yntema, 131, 811 (1963)
E. Kashy and T. W. Conlon (private communication)
R. H. Nussbaum, Rev. Mod. Phys. 28, 423 (1956)
A. M. Morozov, V. V. Remaev, and P. A. Yampol'ski, Zh. Eksperim. i Teor. Fiz. 39, 973 (1960) [English transl.: Soviet Phys.—JETP 12, 674 (1961)]
J. Rapaport, MIT thesis (unpublished)
J. L. Yntema, Phys. Rev. 127, 1659 (1962)
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J. C. Legg and E. Rost (to be published)
B. F. Bayman, J. D. McCullen, and L. Zamick, Phys. Rev. Letters 11, 215 (1963)
D. L. Harris and J. D. McCullen, Phys. Rev. 132, 310 (1963)
E. Brun, J. J. Kraushaar, W. L. Pierce, and W. J. Veigele, Phys. Rev. Letters 9, 166 (1962)
R. D. Lawson, Phys. Rev. 124, 1500 (1961)
R. G. Cornwell (private communication)
L. A. Konig, J. H. W. Mattauch, and A. H. Wapstra, Nucl. Phys. 31, 18 (1962)
B. H. Flowers, Proc. Roy. Soc. (London) A212, 248 (1952)
R. D. Lawson and B. Zeidman, Phys. Rev. 128, 821 (1962)
S. G. Nilsson, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 29, No. 16 (1955)
A. R. Edmonds and B. H. Flowers, Proc. Roy. Soc. (London) A214, 515 (1952)
Omitted endnote
Omitted endnote

[c1] R. D. Lawson and J. L. Uretsky, Phys. Rev. 106, 1369 (1957) I. Talmi, in Proceedings of the Rehovoth Conference on Nuclear Structure (North-Holland Publishing Company, Amsterdam, 1958)

[c2] I. Talmi and I. Unna, Ann. Rev. Nucl. Sci. 10, 353 (1960)

[c3] I. Talmi, Rev. Mod. Phys. 34, 704 (1962)

[c4] A. de-Shalit and I. Talmi, Nuclear Shell Theory (Academic Press Inc., New York, 1963)

[c5] H. A. Jahn, Proc. Roy. Soc. (London) A205, 192 (1951)

[c6] S. P. Pandya, Phys. Rev. 103, 956 (1956) S. Goldstein and I. Talmi, 102, 598 (1956)

[c7] R. H. Bassel, R. M. Drisko, and G. R. Satchler, Oak Ridge National Laboratory Technical Report ORNL-3240, 1962 (unpublished)

[c8] W. Tobocman, Theory of Direct Nuclear Reactions (Oxford University Press, London, 1961)

[c9] P. C. Rogers and G. E. Gordon, Phys. Rev. 129, 2653 (1963)

[c10] N. Sarma (private communication)

[c11] I. Talmi, Phys. Rev. 126, 1096 (1962)

[c12] K. Way et al. in Landolt-Bornstein, New Series, Energy Levels of Nuclei, edited by A. M. Hellwege and K. H. Hellwege (Springer-Verlag, Berlin, 1961), Vol. 1

[c13] H. W. Kendall and I. Talmi, Phys. Rev. 128, 792 (1962) J. Vervier, Phys. Letters 5, 79 (1963) J. E. Schwager, Phys. Rev. 121, 569 (1961) [27]

[c14] G. Bassani, L. Colli, E. Gadioli, and I. Iori, Nucl. Phys. 36, 471 (1962)

[c15] R. R. Wilson, A. A. Bartlett, J. J. Kraushaar, J. D. McCullen, and R. A. Ristinen, Phys. Rev. 125, 1655 (1962) L. T. Dillman, J. J. Kraushaar, and J. D. McCullen, Nucl. Phys. 42, 383 (1963)

[c16] H. O. Funsten, N. R. Roberson, and E. Rost (to be published) B. F. Bayman, H. O. Funsten, N. R. Roberson, E. Rost, and R. Sherr, preliminary report by R. Sherr in Proceedings of The Padua Conference on Direct Interactions and Nuclear Reaction Mechanisms (Gordon and Breach, New York, 1963)

[c17] T. Komoda (to be published)

[c18] G. J. McCallum, A. T. G. Ferguson, and G. S. Mani, Nucl. Phys. 17, 116 (1960) N. O. Lassen and C. Larsen, 43, 183 (1963)

[c19] J. L. Yntema (private communication)

[c20] R. W. Bauer, J. D. Anderson, and L. J. Chrittensen, Phys. Rev. 130, 312 (1963)

[c21] M. H. Macfarlane, B. J. Raz, J. L. Yntema, and B. Zeidman, Phys. Rev. 127, 204 (1962)

[c22] P. C. Simms, N. Benczer-Koller, and C. S. Wu, Phys. Rev. 121, 1169 (1961)

[c23] L. H. Th. Rietjens, O. M. Bilaniuk, and M. H. Macfarlane, Phys. Rev. 120, 527 (1960) J. L. Yntema, 131, 811 (1963)

[c24] E. Kashy and T. W. Conlon (private communication)

[c25] R. H. Nussbaum, Rev. Mod. Phys. 28, 423 (1956)

[c26] A. M. Morozov, V. V. Remaev, and P. A. Yampol'ski, Zh. Eksperim. i Teor. Fiz. 39, 973 (1960) [English transl.: Soviet Phys.—JETP 12, 674 (1961)]

[c27] J. Rapaport, MIT thesis (unpublished)

[c28] J. L. Yntema, Phys. Rev. 127, 1659 (1962)

[c29] M. Hillman, Phys. Rev. 129, 2227 (1963)

[c30] L. W. Nordheim, Rev. Mod. Phys. 23, 322 (1951)

[c31] M. H. Brennan and A. M. Bernstein, Phys. Rev. 120, 927 (1960)

[c32] E. Kashy, Phys. Rev. 134, B378 (1964)

[c33] J. K. Kliwer, J. J. Kraushaar, R. A. Ristinen, J. R. Keith, and A. A. Bartlett, Nucl. Phys. 50, 328 (1963)

[c34] J. C. Legg and E. Rost (to be published)

[c35] B. F. Bayman, J. D. McCullen, and L. Zamick, Phys. Rev. Letters 11, 215 (1963)

[c36] D. L. Harris and J. D. McCullen, Phys. Rev. 132, 310 (1963)

[c37] E. Brun, J. J. Kraushaar, W. L. Pierce, and W. J. Veigele, Phys. Rev. Letters 9, 166 (1962)

[c38] R. D. Lawson, Phys. Rev. 124, 1500 (1961)

[c39] R. G. Cornwell (private communication)

[c40] L. A. Konig, J. H. W. Mattauch, and A. H. Wapstra, Nucl. Phys. 31, 18 (1962)

[c41] B. H. Flowers, Proc. Roy. Soc. (London) A212, 248 (1952)

[c42] R. D. Lawson and B. Zeidman, Phys. Rev. 128, 821 (1962)

[c43] S. G. Nilsson, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 29, No. 16 (1955)

[c44] A. R. Edmonds and B. H. Flowers, Proc. Roy. Soc. (London) A214, 515 (1952)

[c45] Omitted endnote

[c46] Omitted endnote

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Spectroscopy in the Nuclear $1 f_{\frac{7}{2}}$ Shell

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Spectroscopy in the Nuclear $1 f_{\frac{7}{2}}$ Shell