12
1 Introduction: From Bound States to the Continuum
Study of the clustering 3 H, 3 He, 4 He and various multi-neutron clusterization in
the near-threshold configurations and the low-energy reactions with multi-nucleon
projectiles, like the radiative capture of α particle, are the exciting challenges for
future studies.
Applications of the Gamow shell model in both the Slater determinant and
coupled-channel representations which are discussed, among others, for mirror
radiative capture reactions 7 Be(p,γ ), 7 Li(n,γ ) and elastic scattering of deuteron on
4 He, are allowing to grasp essential features of this double approach.
All chapters of this textbook give a fairly compact description of the generalization of the phenomenologically successful shell model in rigged Hilbert space, to
obtain the shell model for open quantum systems. Despite various limitations of this
textbook, we believe that the Gamow shell model deserves further detailed studies
for several reasons.
Firstly, it overcomes the unwanted separation between the nuclear structure
and the nuclear reaction models, what often plagued an understanding of nuclear
phenomena.
Secondly, as the Gamow shell model is an extension of a well-known nuclear
shell model, it could become the workhorse of comprehensive studies of nuclear
structure, allowing to systematize the wealth of data on spectra, transition probabilities, nuclear moments, particle decay, etc.
Thirdly, the Gamow shell model, like its predecessor the traditional shell model,
could become the foundation of many microscopic theories of nuclear structure. The
construction of a realistic interaction for finite nuclei could also be put on a solid
ground once unitarity is respected in calculating the eigenfunctions and eigenvalues.
Finally, as the coupled-channel Gamow shell model is the reaction theory rooted
in the configuration-mixing approach, it could provide a starting point for simpler
approaches, like those using optical potentials, or help to assess importance of
nonlocal effects in nuclear reactions.
References
1. N. Michel, W. Nazarewicz, M. Płoszajczak, T. Vertse, J. Phys. G. Nucl. Part. Phys. 36, 013101
(2009)
2. I.M. Gel’fand, N.Y. Vilenkin, Generalized Functions, vol. 4 (Academic Press, New York, 1961)
3. K. Maurin, Generalized Eigenfunction Expansions and Unitary Representations of Topological
Groups (Polish Scientific Publishers, Warsaw, 1968)
4. A. Bohm, Lecture Notes in Physics, vol. 78 (Springer Verlag, New York, 1978)
5. G. Ludwig, Foundations of Quantum Mechanics , vol. I and II (Springer, New York, 1983)
6. G. Ludwig, An Axiomatic Basis of Quantum Mechanics, vol. I and II (Springer, New York,
1983)
7. A. Bohm, M. Gadella, Lecture Notes in Physics, vol. 348 (Springer, Berlin, 1989)
8. R. de la Madrid, Eur. J. Phys. 26, 287 (2005)
9. R. de la Madrid, J. Math. Phys. 53, 102113 (2012)
10. A. Siegert, Phys. Rev. 56, 750 (1939)
11. J. Halliwell, in Proceedings of the 7th Winter School for Theoretical Physics on Quantum Cosmology and Baby Universes, Israel, December 27–January 4, 1990, ed. by T. P., R. Coleman,
J.B. Hartle, S. Weinberg (World Scientific, Singapore, 1991)
1 Introduction: From Bound States to the Continuum
Study of the clustering 3 H, 3 He, 4 He and various multi-neutron clusterization in
the near-threshold configurations and the low-energy reactions with multi-nucleon
projectiles, like the radiative capture of α particle, are the exciting challenges for
future studies.
Applications of the Gamow shell model in both the Slater determinant and
coupled-channel representations which are discussed, among others, for mirror
radiative capture reactions 7 Be(p,γ ), 7 Li(n,γ ) and elastic scattering of deuteron on
4 He, are allowing to grasp essential features of this double approach.
All chapters of this textbook give a fairly compact description of the generalization of the phenomenologically successful shell model in rigged Hilbert space, to
obtain the shell model for open quantum systems. Despite various limitations of this
textbook, we believe that the Gamow shell model deserves further detailed studies
for several reasons.
Firstly, it overcomes the unwanted separation between the nuclear structure
and the nuclear reaction models, what often plagued an understanding of nuclear
phenomena.
Secondly, as the Gamow shell model is an extension of a well-known nuclear
shell model, it could become the workhorse of comprehensive studies of nuclear
structure, allowing to systematize the wealth of data on spectra, transition probabilities, nuclear moments, particle decay, etc.
Thirdly, the Gamow shell model, like its predecessor the traditional shell model,
could become the foundation of many microscopic theories of nuclear structure. The
construction of a realistic interaction for finite nuclei could also be put on a solid
ground once unitarity is respected in calculating the eigenfunctions and eigenvalues.
Finally, as the coupled-channel Gamow shell model is the reaction theory rooted
in the configuration-mixing approach, it could provide a starting point for simpler
approaches, like those using optical potentials, or help to assess importance of
nonlocal effects in nuclear reactions.
References
1. N. Michel, W. Nazarewicz, M. Płoszajczak, T. Vertse, J. Phys. G. Nucl. Part. Phys. 36, 013101
(2009)
2. I.M. Gel’fand, N.Y. Vilenkin, Generalized Functions, vol. 4 (Academic Press, New York, 1961)
3. K. Maurin, Generalized Eigenfunction Expansions and Unitary Representations of Topological
Groups (Polish Scientific Publishers, Warsaw, 1968)
4. A. Bohm, Lecture Notes in Physics, vol. 78 (Springer Verlag, New York, 1978)
5. G. Ludwig, Foundations of Quantum Mechanics , vol. I and II (Springer, New York, 1983)
6. G. Ludwig, An Axiomatic Basis of Quantum Mechanics, vol. I and II (Springer, New York,
1983)
7. A. Bohm, M. Gadella, Lecture Notes in Physics, vol. 348 (Springer, Berlin, 1989)
8. R. de la Madrid, Eur. J. Phys. 26, 287 (2005)
9. R. de la Madrid, J. Math. Phys. 53, 102113 (2012)
10. A. Siegert, Phys. Rev. 56, 750 (1939)
11. J. Halliwell, in Proceedings of the 7th Winter School for Theoretical Physics on Quantum Cosmology and Baby Universes, Israel, December 27–January 4, 1990, ed. by T. P., R. Coleman,
J.B. Hartle, S. Weinberg (World Scientific, Singapore, 1991)