Abstract
The review is concerned with studies of one-nucleon and two-nucleon halos in isobar analog states of light nuclei with \(A = 6,\,\,12,\,\,13,\,\,14\). The study allow us to investigate manifestations of isotopic invariance in new objects and to relate properties of the neutrino and proton halos. The existence of a halo in isobar analog states has been little studied experimentally so far. It is proposed to solve the problem of experimentally determining the radii of some possible halo states in nuclei from 6Li to 14O that make up isobar analog doublets and triplets. New possible halo candidates are found in the 13C and 13N mirror nuclei, in the \(A\) = 12 and \(A\) = 14 isobar analog multiplets. Note that the isobar analog states with \(T = 1\) in the \(A = 12\) triplet are experimentally investigated for the first time in the transfer and charge-exchange reactions. It is established that the root-mean-square radii of the \({{0}^{ + }}\) states in the \(A = 6\) multiplet coincide within errors. The results are obtained by two independent methods, ANC and MDM.
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REFERENCES
I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N. Yoshikawa, K. Sugimoto, O. Yamakawa, T. Kobayashi, and N. Takahashi, “Measurements of interaction cross-sections and nuclear radii in the light p-shell region,” Phys. Rev. Lett. 55, 2676–2679 (1985).
A. I. Baz, “Threshold effects in nuclear reactions,” Adv. Phys. 8, 349–374 (1959).
T. Otsuka, N. Fukunishi, and H. Sagawa, “Structure of exotic neutron-rich nuclei,” Phys. Rev. Lett. 70, 1385–1388 (1993).
T. L. Belyaeva, R. Perez-Torres, A. A. Ogloblin, A. S. Demyanova, S. N. Ershov, and S. A. Goncharov, “Determination of neutron halo radii in the first excited states of 13C and 11Be with the asymptotic normalization coefficients method,” Phys. Rev. C 90, 064610 (2014).
I. Tanihata, H. Savajols, and R. Kanungo, “Recent experimental progress in nuclear halo structure studies,” Prog. Part. Nucl. Phys. 68, 215–313 (2013).
A. A. Ogloblin, A. N. Danilov, T. L. Belyaeva, A. S. Demyanova, S. A. Goncharov, and W. Trzaska, “Observation of abnormally large radii of nuclei in excited states in the vicinity of neutron thresholds,” Phys. At. Nucl. 74, 1548–1561 (2011).
A. A. Ogloblin, A. N. Danilov, T. L. Belyaeva, A. S. Demyanova, S. A. Goncharov, and W. Trzaska, “Effect of neutron halos on excited states of nuclei,” Phys. Rev. C 84, 054601 (2011).
K. Riisager, “Halos and related structures,” Phys. Scr. 152, 014001 (2013). arXiv:1208.6415 [nucl-ex].
F. Kobayashi and Y. Kanada-En’yo, “Novel cluster states in 10Be,” Phys. Rev. C 86, 064303 (2012). arXiv: 1208.0387 [nucl-th].
A. S. Demyanova, A. A. Ogloblin, A. N. Danilov, T. L. Belyaeva, S. A. Goncharov, and W. Trzaska, “Proton halo in the 13N nucleus,” JETP Lett. 104, 526–530 (2016).
T. Minamisono, T. Ohtsubo, I. Minami, S. Fukuda, A. Kitagawa, M. Fukuda, K. Matsuta, Y. Nojiri, S. Takeda, H. Sagawa, and H. Kitagawa, “Proton halo of 8B disclosed by its giant quadrupole moment,” Phys. Rev. Lett. 69, 2058–2061 (1992).
F. Negoita, C. Borcea, F. Carstoiu, M. Lewitowicz, M. G. Saint-Laurent, R. Anne, D. Bazin, J. M. Corre, P. Roussel-Chomaz, V. Borrel, D. Guillemaud-Mueller, H. Keller, A. C. Mueller, F. Pougheon, O. Sorlin, S. Lukyanov, Y. Penionzhkevich, A. Fomichev, N. Skobelev, O. Tarasov, Z. Dlouhy, and A. Kordyasz, “8B proton halo via reaction and breakup cross section measurements,” Phys. Rev. C 54, 1787–1797 (1996).
R. Lewis and A. C. Hayes, “Deuteron stripping as a probe of the proton halo in 17F,” Phys. Rev. C 59, 1211–1214 (1999).
Z. Dongmei, Z. Yongnan, Y. Daqing, Z. Xizhen, Z. Yi, T. Minamisono, M. Matsuta, M. Fukuda, M. Mihara, Z. Chunlei, W. Zhiqiang, D. Enpeng, L. Hailong, X. Guoji, and Z. Shengyun, “Quadrupole moment and a proton halo structure in 17F(Iπ = 5/2+),” J. Phys. G: Nucl. Phys. 34, 523–528 (2007).
E. Ryberg, C. Forssén, H. W. Hammer, and L. Platter, “Effective field theory for proton halo nuclei,” Phys. Rev. C 89, 014325 (2014). arXiv:1308.5975 [nucl-th].
A. S. Demyanova, A. A. Ogloblin, S. A. Goncharov, A. N. Danilov, T. L. Belyaeva, and W. Trzaska, “Use of (3He, t) charge-exchange reactions in determining radii of excited states of nuclei,” Phys. Atom. Nucl. 80, 831–837 (2017).
A. N. Danilov, T. L. Belyaeva, A. S. Demyanova, S. A. Goncharov, and A. A. Ogloblin, “Determination of nuclear radii for unstable states in 12C with diffraction inelastic scattering,” Phys. Rev. C 80, 054603 (2009).
A. A. Ogloblin, A. N. Danilov, A. S. Demyanova, S. A. Goncharov, T. L. Belyaeva, and W. Trzaska, “Nuclear Particle Correlations and Cluster Physics,” in Nuclear Particle Correlations and Cluster Physics, Ed. by W.-U. Schröder (2017), pp. 311–338.
J. S. Blair, “Inelastic diffraction scattering,” Phys. Rev. 115, 928–938 (1959).
G. R. Satchler, Introduction to Nuclear Reactions, 2nd ed. (Macmillan Education, UK, 1990)
A. Lane, “Isobaric spin dependence of the optical potential and quasielastic (p, n) reactions,” Nucl. Phys. A 35, 676–685 (1962).
A. S. Demyanova, A. N. Danilov, A. A. Ogloblin, V. I. Starastsin, S. V. Dmitriev, W. H. Trzaska, S. A. Goncharov, T. L. Belyaeva, V. A. Maslov, Yu. G. Sobolev, Y. E. Penionzhkevich, S. V. Khlebnikov, G. P. Tyurin, N. Burtebaev, D. Janseitov, Y. B. Gurov, J. Louko, and V. M. Sergeev, “States of the 12N nucleus with increased radii,” JETP Lett. 111, 409–415 (2020).
A. S. Demyanova, A. N. Danilov, A. A. Ogloblin, S. A. Goncharov, T. L. Belyaeva, W. H. Trzaska, and V. I. Starastsin, “Search for signs of neutron and proton halos in the isobaric analog excited states of A = 14 nuclei,” JETP Lett. 112, 463–470 (2020).
L. D. Blokhintsev, I. Borbely, and E. I. Dolinskii, Sov. J. Part. Nucl. 8, 485–535 (1977).
G. R. Satchler, Direct Nuclear Reactions (Clarendon Press, Oxford, 1983).
Z. H. Liu, C. J. Lin, H. Q. Zhang, Z. C. Li, J. S. Zhang, Y. W. Wu, F. Yang, M. Ruan, J. C. Liu, S. Y. Li, and Z. H. Peng, “Asymptotic normalization coefficients and neutron halo of the excited states in 12B and 13C,” Phys. Rev. C 64, 034312 (2001).
D. Y. Pang and A. M. Mukhamedzhanov, “Asymptotic normalization coefficients and spectroscopic factors from deuteron stripping reactions,” Phys. Rev. C 90, 044611 (2014).
M. McCleskey, A. M. Mukhamedzhanov, L. Trache, R. E. Tribble, A. Banu, V. Eremenko, V. Z. Goldberg, Y. W. Lui, E. McCleskey, B. T. Roeder, A. Spiridon, F. Carstoiu, V. Burjan, Z. Hons, and I. J. Thompson, “Determination of the asymptotic normalization coefficients for 14C + n ↔ 15C, the 14C (n,γ) 15C reaction rate, and evaluation of a new method to determine spectroscopic factors,” Phys. Rev. C 89, 044605 (2014).
B. Jonson, “Light dripline nuclei,” Phys. Rep. 389, 1–59 (2004).
C. T. Liang, X. H. Li, and C. H. Cai, “Global 3He optical model potential below 270 MeV,” J. Phys. G: Nucl. Phys. 36, 085104 (2009).
Y. Zhang, D. Y. Pang, and J. L. Lou, “Optical model potential for deuteron elastic scattering with 1p-shell nuclei,” Phys. Rev. C 94, 014619 (2016). arXiv: 1606.01507.
S. A. Goncharov, O. M. Knyaz’kov, and A. A. Kolozhvari, “Isospin dependence of nucleus-nucleus interaction from data on scattering of isobaric nuclei,” Phys. At. Nucl. 59, 634–646 (1996).
D. T. Khoa and G. R. Satchler, “Generalized folding model for elastic and inelastic nucleus-nucleus scattering using realistic density dependent nucleon-nucleon interaction,” Nucl. Phys. A 668, 3–41 (2000).
D. T. Khoa, G. R. Satchler, and W. von Oertzen, “Nuclear incompressibility and density dependent NN interactions in the folding model for nucleus-nucleus potentials,” Phys. Rev. C 56, 954–969 (1997).
S. A. Goncharov, G. Kazacha, and N. Timofeyuk, Preprint No. JINR P4-87-262 (JINR, Dubna, 1987).
B. Sommer and J. G. Zabolitzky, “On numerical Bessel transformation,” Comput. Phys. Commun. 16, 383–387 (1979). https://www.sciencedirect.com/science/ article/pii/0010465579900444.
O. M. Knyazkov and A. A. Kolozhvary, Izv. Ross. Akad. Nauk, Ser. Fiz. 57, 48–53 (1993).
S. A. Goncharov and A. Izadpanah, “Nucleus-nucleus potential within the semimicroscopic dispersive model on the basis of a corrected folding model potential,” Phys. Atom. Nucl. 70, 18–28 (2007).
S. A. Goncharov and A. Izadpanah, “Dispersive semimicroscopic analysis of nuclear-nuclear collisions on the basis of a corrected folding-model potential,” Phys. Atom. Nucl. 70, 1491–1499 (2007). https://doi.org/10.1134/S1063778807090037
S. A. Goncharov and R. V. Sukhorukov, “An approximation for the density matrix in calculations of the mean-field potential of the interaction of nuclei,” Moscow Univ. Phys. Bull. 73, 301–305 (2018). https://doi.org/10.3103/S0027134918030074
P. D. Kunz and E. Rost, “The Distorted-Wave Born Approximation,” in Computational Nuclear Physics 2: Nuclear Reactions, Ed. by K. Langanke, J. A. Maruhn, and S. E. Koonin (Springer, New York, 1993), pp. 88–107.
I. J. Thompson, “Coupled reaction channels calculations in nuclear physics,” Comput. Phys. Rep. 7, 167–212 (1988).
T. L. Belyaeva, S. A. Goncharov, A. S. Demyanova, A. A. Ogloblin, A. N. Danilov, V. A. Maslov, Yu. G. Sobolev, W. Trzaska, S. V. Khlebnikov, G. P. Tyurin, N. Burtebaev, D. Janseitov, and E. Mukhamejanov, “Neutron halos in the excited states of 12B,” Phys. Rev. C 98, 034602 (2018). https://link.aps.org/doi/10.1103/PhysRevC.98.034602
T. L. Belyaeva, N. Zelenskaya, and N. Odintsov, “Computation of correlation characteristics of nuclear reactions induced by semi-heavy ions,” Comput. Phys. Commun. 73, 161–169 (1992). https:// www.sciencedirect.com/science/article/pii/001046559290036X.
G. Satchler, “Isospin and macroscopic models for the excitation of giant resonances and other collective states,” Nucl. Phys. A 472, 215–236 (1987). https://www.sciencedirect.com/science/article/pii/0375947487902089.
A. S. Demyanova, A. N. Danilov, S. V. Dmitriev, A. A. Ogloblin, T. L. Belyaeva, N. Burtebaev, P. Drobyshev, S. A. Goncharov, Yu. B. Gurov, P. Heikkinen, R. Julin, S. V. Khlebnikov, V. A. Maslov, N. Nassurlla, Y. E. Penionzhkevich, Yu. G. Sobolev, W. Trzaska, G. P. Tyurin, and V. I. Zherebchevskii, “Spectroscopy of exotic states of 13C,” EPJ Web Conf. 66, 02027 (2014).
T. Yamada and Y. Funaki, “Cluster states and alpha particle condensation in 13C,” Int. J. Mod. Phys. E 17, 2101–2105 (2008). https://doi.org/10.1142/S0218301308011161
Z. Y. Liu, C. B. Li, S. G. Wang, J. Zhou, Q. I. Meng, S. J. Lu, and S. H. Zhou, “Measurement of change of 7Be decay rate in Be and Au,” Chin. Phys. Lett. 30, 829 (2003). arXiv:nucl-ex/0306002.
R. J. Peterson, J. R. Shepard, and R. A. Emigh, “Isoscalar and isovector transition amplitudes in A = 13,” Phys. Rev. C 24, 826–840 (1981). https://link.aps.org/doi/10.1103/PhysRevC.24.826
A. S. Demyanova, A. A. Ogloblin, S. N. Ershov, F. A. Gareev, R. S. Kurmanov, E. F. Svinareva, S. A. Goncharov, V. V. Adodin, N. Burtebaev, J. M. Bang, and J. S. Vaagen, “Rainbows in nuclear reactions and the optical potential,” Phys. Scr. 32, 89–106 (1990). https://doi.org/10.1088/0031-8949/1990/t32/015
A. S. Demyanova, V. I. Starastsin, A. N. Danilov, A. A. Ogloblin, S. V. Dmitriev, S. A. Goncharov, T. L. Belyaeva, V. A. Maslov, Y. G. Sobolev, W. Trzaska, P. Heikkinen, G. P. Gurov, N. Burtebaev, and D. Janseitov, “Possible neutron and proton halo structure in the isobaric analog states of A = 12 nuclei,” Phys. Rev. C 102, 054612 (2020).
A. Demyanova, V. Starastsin, A. Ogloblin, A. Danilov, S. Dmitriev, W. Trzaska, P. Heikkinen, T. Belyaeva, S. Goncharov, V. Maslov, Yu. Sobolev, Yu. Gurov, B. Chernyshev, N. Burtebaev, D. Janseitov, and S. Khlebnikov, “The spin-parities of the 13.35 MeV state and high-lying excited states around 20 MeV in 12C nucleus,” Eur. Phys. J. A 57, 204 (2021). https://doi.org/10.1140/epja/s10050-021-00515-7
W. Trzaska, P. Heikkinen, A. Danilov, A. Demyanova, S. Khlebnikov, T. Malamut, V. Maslov, A. Ogloblin, and Yu. Sobolev, “High-resolution scattering experiments at the K130 cyclotron in Jyväskylä,” Nucl. Instrum. Methods Phys. Res., Sect. A 903, 241–245 (2018). https://doi.org/10.1016/j.nima.2018.07.002
G. C. Ball and J. Cerny, “Microscopic analysis of the (3He, t) and (3He, 3He’) reactions on 1 p-shell nuclei,” Phys. Rev. 177, 1466 (1969).
W. A. Sterrenburg, M. N. Harakeh, S. Y. Van Der Werf, and A. Van Der Woude, “Excitation and Decay of ΔL = 1 modes in 12N via the reaction,” Nucl. Phys. A 405, 109–125 (1983). https://doi.org/10.1016/0375-9474(83)90326-3
I. Tanihata, T. Kobayashi, O. Yamakawa, S. Shimoura, K. Ekuni, K. Sugimoto, N. Takahashi, T. Shimoda, and H. Sato, “Measurement of interaction cross sections using isotope beams of Be and B and isospin dependence of the nuclear radii,” Phys. Lett. B 206, 592–596 (1988). https://doi.org/10.1016/0370-2693(88)90702-2
A. Ozawa, I. Tanihata, T. Kobayashi, D. Hirata, O. Yamakawa, K. Omata, N. Takahashi, T. Shimoda, K. Sugimoto, D. Olson, W. Christie, and H. Wieman, “Interaction cross-sections and radii of 11C and 12N, and effective deformation parameters in light mirror nuclei,” Nucl. Phys. A 583, 807–810 (1995). https:// www.sciencedirect.com/science/article/pii/037594749 400763D.
R. Peterson, H. Bhang, J. Hamill, and T. Masterson, “The 14C(α, α') 14C and 13C(d, p)14C reactions,” Nucl. Phys. A 425, 469–492 (1984). https://www.sciencedirect.com/science/article/pii/0375947484900204.
L. Zu-Hua, “Halo Nature of 14C, 15C,” Chin. Phys. Lett. 19, 1071–1073 (2002). https://doi.org/10.1088/0256-307x/19/8/313
R. Peterson and J. Hamill, “Proton stripping to 14N,” Nucl. Phys. A 362, 163–172 (1981). https://www.sciencedirect.com/science/article/pii/0375947481906758.
A. Ozawa, T. Suzuki, and I. Tanihata, “Nuclear size and related topics,” Nucl. Phys. A 693, 32–62 (2001). https://www.sciencedirect.com/science/article/pii/S037 5947401011526.
G. C. Ball and J. Cerny, “14N(3He, t)14O reaction and excited isospin triads in mass 14,” Phys. Rev. 155, 1170–1176 (1967). https://link.aps.org/doi/10.1103/PhysRev.155.1170
A. Negret, T. Adachi, and B. R. Barrett, C. Bäumer, A. M. Van Den Berg, G. P. A. Berg, P. Von Brentano, D. Frekers, D. De Frenne, H. Fujita, K. Fujita, Y. Fujita, E. W. Grewe, P. Haefner, M. N. Harakeh, K. Hatanaka, K. Heyde, M. Hunyadi, E. Jacobs, Yu. Kalmykov, A. Korff, K. Nakanishi, P. Navrátil, P. Von Neumann-Cosel, L. Popescu, S. Rakers, A. Richter, N. Ryezayeva, Y. Sakemi, A. Shevchenko, Y. Shimbara, Y. Shimizu, Y. Tameshige, A. Tamii, M. Uchida, J. Vary, H. J. Wörtche, M. Yosoi, and L. Zamick, “Gamow-Teller strengths in the A = 14 multiplet: A challenge to the shell model,” Phys. Rev. Lett. 97, 062502 (2006). https://link.aps.org/doi/10.1103/PhysRevLett.97.062502
S. Mezhevych, A. Rudchik, K. Rusek, A. Budzanowski, B. Czech, J. Choiński, L. Glowacka, S. Kliczewski, E. Koshchy, V. Kyryanchuk, A. Mokhnach, A. Rudchik, S. Sakuta, R. Siudak, I. Skwirczyńska, and A. Szczurek, “Excitation of 14C by 45 MeV 11B ions,” Nucl. Phys. A 753, 13–28 (2005). https:// www.sciencedirect.com/science/article/pii/S0375947405002666.
V. Kukulin, V. Pomerantsev, K. Razikov, V. Voronchev, and G. Ryzhikh, “Detailed study of the cluster structure of light nuclei in a three-body model (IV). Large space calculation for A = 6 nuclei with realistic nuclear forces,” Nucl. Phys. A 586, 151–189 (1995). https:// www.sciencedirect.com/science/article/pii/03759474940 04948.
F. Robicheaux, “Simple asymptotic potential model for finding weakly bound negative ions,” Phys. Rev. A 60, 1706–1709 (1999). https://link.aps.org/doi/10.1103/PhysRevA.60.1706
A. S. Jensen, K. Riisager, D. V. Fedorov, and E. Garrido, “Structure and reactions of quantum halos,” Rev. Mod. Phys. 76, 215–261 (2004). https://link.aps.org/doi/10.1103/RevModPhys.76.215
I. N. Izosimov, “Structure of β-decay strength function S β(E) in halo nuclei,” Phys. Part. Nucl. Lett. 15, 621–626 (2018). https://doi.org/10.1134/s1547477118060092
K. Arai, Y. Suzuki, and K. Varga, “Neutron-proton halo structure of the 3.563-MeV 0+ State in 6Li,” Phys. Rev. C 51, 2488–2493 (1995). https://link.aps.org/doi/10.1103/PhysRevC.51.2488
K. Arai, Y. Ogawa, Y. Suzuki, and K. Varga, “Structure of the mirror nuclei 9Be and 9B in a microscopic cluster model,” Phys. Rev. C 54, 132–146 (1996). https://link.aps.org/doi/10.1103/PhysRevC.54.132
Y. Suzuki, “The ground-state structure and the soft dipole mode of the 6He nucleus,” Nucl. Phys. A 528, 395–408 (1991). https://doi.org/10.1016/0375-9474(91)90095-n
M. V. Zhukov, L. V. Chulkov, B. V. Danilin, and A. A. Korsheninnikov, “Specific structure of the 6He nucleus and fragmentation experiments,” Nucl. Phys. A 533, 428–440 (1991). https://doi.org/10.1016/0375-9474(91)90526-c
T. Kobayashi, O. Yamakawa, K. Omata, K. Sugimoto, T. Shimoda, N. Takahashi, and I. Tanihata, “Projectile fragmentation of the extremely neutron-rich nucleus 11Li at 0.79 GeV/nucleon,” Phys. Rev. Lett. 60, 2599–2602 (1988). https://link.aps.org/doi/10.1103/PhysRevLett.60.2599
G. Alkhazov, A. Dobrovolsky, P. Egelhof, H. Geissel, H. Irnich, A. Khanzadeev, G. Korolev, A. Lobodenko, G. Münzenberg, M. Mutterer, S. Neumaier, W. Schwab, D. Seliverstov, T. Suzuki, and A. Vorobyov, “Nuclear matter distributions in the 6He and 8He nuclei from differential cross sections for small-angle proton elastic scattering at intermediate energy,” Nucl. Phys. A 712, 269–299 (2002). https://www.sciencedirect.com/science/article/pii/S0375947402012733
A. S. Demyanova, A. A. Ogloblin, A. N. Danilov, T. L. Belyaeva, S. A. Goncharov, P. N. Terekhin, and R. V. Sukhorukov, “Possible existence of neutron-proton halo in6Li,” KnE Energy 3, 1 (2018). https://doi.org/10.18502/ken.v3i1.1715
R. Givens, M. Brussel, and A. Yavin, “An experimental study of 3He elastic, inelastic and charge-exchange scattering from 6Li,” Nucl. Phys. A 187, 490–500 (1972). https://www.sciencedirect.com/science/article/pii/0375947472906744.
S. Sakuta, N. Burtebayev, J. Burtebayeva, A. Duise-bayev, N. Glushchenko, M. Nassurlla, A. Amar, S. Artemov, S. Kliczewski, E. Piasecki, K. Rusek, R. Siudak, A. Trzcińska, and M. Wolińska-Cichocka, “The channel coupling and triton cluster exchange effects in 3He scattering on 6Li nuclei,” Acta Phys. Pol. B 45, 1853 (2014). https://doi.org/10.5506/aphyspolb.45.1853
N. Burtebayev, J. Burtebayeva, N. Glushchenko, Z. Kerimkulov, A. Amar, M. Nassurlla, S. Sakuta, S. Artemov, S. Igamov, A. Karakhodzhaev, K. Rusek, and S. Kliczewski, “Effects of t- and α-transfer on the spectroscopic information from the 6Li (3He,d)7Be reaction,” Nucl. Phys. A 909, 20–35 (2013). https:// www.sciencedirect.com/science/article/pii/S0375947413 004880.
O. Bochkarev, L. Chulkov, A. Korsheninnikov, E. Kuz’min, I. Mukha, and G. Yankov, “Democratic decay of 6Be states,” Nucl. Phys. A 505, 215–240 (1989). https://www.sciencedirect.com/science/article/pii/0375947489903710.
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Demyanova, A.S., Danilov, A.N., Dmitriev, S.V. et al. Investigation of Halos in Isobar Analog States. Phys. Part. Nuclei 55, 233–255 (2024). https://doi.org/10.1134/S1063779624020035
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DOI: https://doi.org/10.1134/S1063779624020035