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Investigations of few-nucleon systems

As it is known, there is still no generally accepted theory of the strong interaction. Important results in this area can be obtained with the investigations of the interaction of neutrons with the lightest nuclei - protons, deuterons, 3He, others. One of the most important results obtained by F.L. Shapiro was the investigation of the energy dependence of the cross section of the  reaction and the prediction of the occurrence of the excited level of 4He with 0+spin. In the 1970-1980s of the last century, these investigations were still carried out under the supervision of E.I. Sharapova.  

To describe the properties of the lightest nuclei, it is necessary to study the NN interaction. At low energies, the interaction of nucleons occurs with an orbital momentum l = 0, that is, in the S-state. Since the spins of the neutron and proton are equal to 1/2, np-interaction is possible in the singlet (1S0) and triplet (3S1) states. The triplet spin state corresponds to the isotopic spin T = 0. In this state, there is a bound state of the neutron and proton - the deuteron with a bond energy of 2224 keV. Pairs of identical particles can only interact in the singlet 1S0 state, since the triplet state is prohibited by the Pauli principle. The interaction in the 1S0 state for the three possible pairs of nucleons (nn, np and pp) corresponds to the interaction with isotopic spin T = 1.

For NN interactions at low energies, the theory of effective radius (TER) was developed. According to TER, the interaction amplitude F for a certain spin state can be expressed in terms of two parameters: the scattering length a and the effective radius r0.


Scattering lengths and effective radii for np and pp interactions are measured with good accuracy. Determining the parameters of the nn interaction is a much more difficult task, since there is no neutron target.

NN interaction in the singlet state at very low energies is described using the so-called virtual level, the physical meaning of which is unclear. Based on ideas about the virtual level, it was concluded that the singlet deuteron does not occur. However, a strict scattering theory does not prohibit the occurrence of a bound state of two nucleons in a singlet state. Currently, the theory of strong interactions is based on quantum chromodynamics. Recently, a number of research papers have been presented that essentially predict the occurrence of a bound state of two nucleons in the 1S0 -state [1-4].

The interaction of neutrons with protons in the 1S0 -state can be described using resonance with negative energy. The resonance energy is determined by the scattering length a and the effective radius r0:


This formula was first obtained by S.T. Ma in 1953 [5]. Since the singlet scattering length is negative, the resonance energy is also negative, that is, the resonance is below the deuteron photodisintegration threshold. The interaction of nucleons in the singlet state can be considered as a manifestation of dibaryon resonance [6-8]. The following estimate of the MeV resonance energy was obtained in [9] that is consistent with formula (2).

If this is a subthreshold resonance (that is, a short-lived quasi-stationary state), then the following processes are possible: a) emission of a cascade of gamma quanta after the capture of neutrons by protons; b) resonant scattering of gamma quanta using deuterons. The idea of ​​describing the interaction of neutrons with nuclei using resonances with negative energy is widely used in neutron physics. F. L. Shapiro and his co-authors applied this idea to describe the interaction of neutrons with 3He that subsequently results in the discovery of the excited level of 4He.

Thus, at present, the task of searching for a dineutron and a singlet deuteron, that is, bound states of two neutrons and a neutron and a proton with a common spin of zero, becomes increasingly urgent. Due to the principle of isotopic invariance, their energies should be close (see Fig. 1). There is apparently no bound state of the two protons, since there is Coulomb repulsion between them. A singlet deuteron can manifest itself in the radiative capture of neutrons by protons with the release of a cascade of two gamma rays. The cross section of such a process is about 104 times smaller than the cross section with the emission of one gamma quantum corresponding to the main transition. We have made attempts to search for such a process. The measurements were carried out in Budapest [10]. In the spectrum of gamma rays there are lines that can be interpreted as a manifestation of the cascade [11]. Their further research is required.

Fig. 1. Sum of masses of different pairs of nucleons and the expected position of the singlet state

The idea of ​​the occurrence of a dineutron was presented back in 1948 by N. Fizer [12]. He estimated the dineutron lifetime (1-5 sec) and the maximum bond energy (3 MeV). An estimate of the bond energy was obtained from the condition of β-decay of a dineutron into a deuteron. To date, a range of experimental indications have been obtained in favor of the occurrence of the dineutron [13-20].

A dineutron can occur in the  reaction. FLNP staff members have proposed a way to search for this reaction and to determine the bond energy of a dineutron by registering a proton in a counter filled with deuterium [21].

The problem of the occurrence of a dineutron is related to the problem of the occurrence of neutral nuclei. A number of interesting results have also been obtained in this area recently [22–26]. It should be noted that according to a number of theoretical papers, the occurrence of neutral nuclei is impossible without the occurrence of a dineutron.  

Thus, at present, there are a number of papers dedicated to this topic and new experiments will be carried out.


  1. F.J. Dyson, Nguen-Huu Xuong, “Y=2 states in SU(6) theory”, Phys. Rev. Lett., v. 13, No. 26, p.815, 1964;
  2. Maltman, N. Isgur, “Nuclear physics and the quark model: Six quarks with chromodynamics”, Phys. Rev., V. D29, p. 952, 1984;
  3. Ivanov A. N., Cargneli M., Farber M., Fuhrmann H., Ivanova V. A., Marton J., Troitskaya N. I.,  Zmeskal J., “Quantum Field Theoretic Model of Metastable Resonant Spin-Singlet State of the np Pair”, e-ArXiv: nucl-th/0407079, 2004;
  4. Yamazaki, Y. Kuramashi, A. Ukawa, “Two-Nucleon Bound States in Quenched Lattice QCD”, Phys. Rev., D84, 054506, 2011;
  5. S.T. Ma, “Interpretation of the Virtual Level of the Deuteron”, Rev. Mod. Phys., v.25, p.853, 1953;
  6. С.Б. Борзаков, “Взаимодействие нейтронов низких энергий с протонами и возможность существования резонанса с  Jπ  = 0+”, Сообщение ОИЯИ P15-93-29,  Дубна, 1989;
  7.  С.Б. Борзаков,  “NN взаимодействие в 1S0 состоянии: виртуальный уровень или дибарионный резонанс?”, Ядерная физика, т.  57, с. 517, 1994;
  8. Hackenburg, Preprints BNL, BNL-77482-2007-IR; “Low-Energy Neutron-Proton Interaction and the Deuterons as Dibaryons: an Empirical Effective-Field View”, Report BNL-77483-2007-JA, 2007;
  9. G.M. Hale, L.S. Brown, M.W. Paris, “Effective field theory as a limit of R-matrix theory for light nuclear reactions”, Phys. Rev. C89, 014623, 2014.
  10. Belgya, S.B. Borzakov, M. Jentschel, M. Maroti, Yu.N. Pokotilovski, L. Szentmiklosi, “Experimental search for the bound-state singlet deuteron in the radiative n-p capture”, ISINN-26, Xi’an, China, May 28-June 1, 2018, Presentation A10; Phys. Rev. C99, 044001, 2019;
  11. S.B. Borzakov, E-Arxive, nucl-ex, 2105.10286, 2021;
  12. Feather, Nature (London), “Properties of a Hypothetical dineutron”, 162, p. 213, 1948;
  13. Sakisaka, M. Tomita, “Experiments on Possible Existence of a Bound Di-Neutron”, J. Phys. Soc. Japan, v. 16, p. 2597-2598, 1961;
  14. O.V. Bochkarev, A.A. Korsheninnikov, E.A. Kuz’min, I.G. Mukha, A.A. Ogloblin, L.V. Chulkov, G.B. Yan’kov, ““Dineutron” emission from an excited state of the 6He nucleus”, Pis’ma Zh. Eksp. Teor. Fiz, 42, No. 7, p. 303-305, 1985; О.В. Бочкарев и др., “Трёхчастичный распад  2+ состояний 6He, 6Li и 6Be”, Ядерная физика, т. 46, с. 12, 1987;
  15. K.K. Seth, B. Parker, “Evidence for dineutrons in extremely neutron-rich nuclei”,  Phys. Rev. Lett., 66(19), p. 2448, 1991;
  16. С. Détraz, “Possible existence of bound neutral nuclei”, Phys. Lett., 66B, 333-336, 1977;
  17. M. Kadenko, “Possible observation of the dineutron in the 159Tb(n,2n)158gTb nuclear reaction”, EPL, 114 , 42001, 2016;
  18. I.M. Kadenko, B. Biro, A. Fenyvesi, “Satistically significant observation of and cross sections for a new nuclear reaction channel on 197Au with bound dineutron escape”, ArXiv 1906. 10755, 2020;
  19. Spyrou, Z. Kohley, D. Basin, B.A. Brown, G. Christian, P.A. DeYoung, J.E. Fink, N. Frank, E. Lundenberg, S. Mosby, W.A. Peters, A. Schiller, J.K. Smith, J. Snyder, M.J. Strongman, M. Thoennessen, A. Volya, “First Observation of Ground State Dineutron Decay 16Be”, Phys. Rev. Lett., 108, 102501, 2012;
  20. Hagino, H. Sagawa, “Correlated two-neutron emission in the decay of unbound nucleus 26O”, ArXiv: nucl-th 1307.55021v1, 2013;
  21. C.Б. Борзаков, Ц. Пантелеев, А.В. Стрелков, “Поиск динейтрона во взаимодействии нейтронов с дейтронами”, Письма в ЭЧАЯ, 2002, № 2[111], с. 45;
  22. F.M. Marques et al., “Detection of Neutron Clasters”, Phys. Rev. C65, 044006, 2002;
  23. Б.Г. Новацкий, Е.Ю. Никольский, С.Б. Сакута, Д.И. Степанов, “Возможное обнаружение легких нейтральных ядер в делении 238U α-частицами”, Письма в ЖЭТФ, т. 96, вып. 5, с. 310-314, 2012;
  24. Б.Г. Новацкий, С.Б. Сакута, Д.Н. Степанов, “Обнаружение легких нейтральных ядер в делении 238U α-частицами методом активации изотопа 27Al”, Письма в ЖЭТФ, т. 98, вып. 11, с. 747-751, 2013;
  25. Th. Faestermann, A. Bergmaier, R. Gernhauser, D. Koll, M. Mahgoub, “Indications for a bound tetraneutron”, Phys. Lett. B824, 136799, 2022;
  26. Duer et al. “Observation of a correlated free four-neutron system”, Nature, 606, p.678, 2022;