CC BY
25LASER INFLUENCE ON NUCLEAR REACTIONS
Ayryan E.A.
LIT, Joint Institute for Nuclear Research, Dubna, Russia
Gevorkyan A.S.
Institute for Informatics and Automation Problems, Yerevan, Armenia
Hnatic M.
Institute of Experimental Physics SAS, Kosice, Slovakia, Joint Institute for Nuclear Research, Dubna, Russia, Faculty of Sciences, P. J. Safarik University, Kosice, Slovakia
Kopcansky P.
Institute of Experimental Physics SAS, Kosice, Slovakia
Oganesyan K.B.
A. Alikhanyan National Lab, Yerevan Physics Institute, Yerevan, Armenia
Papoyan V.V.
Joint Institute for Nuclear Research, Dubna, Russia
Rostovtsev Yu.V. University of North Texas, Denton, TX, USA
Timko M.
Institute of Experimental Physics SAS, Kosice, Slovakia
Abstract
For the compound nucleus the induced nuclear reactions are considered for s neutrons near p resonances in the presence of a strong electromagnetic field . The cross sections as functions of the resonance parameters and the laser-radiation power are found.
Keywords: laser; nuclear reaction, neutron; cross section
1. INTRODUCTION
The field of laser induced nuclear reactions is an exciting and rapidly expanding new branch of physics. In the near future high power lasers are predicted to be used e.g. for isotope production in nuclear medicine and in biological and material sciences. Furthermore this kind of laser could be used as an injector for large scale ion accelerators and to provide high intensity proton beams for the transmutation of radioactive waste. Novel petawatt laser facilities are able to accelerate ion species with A ~ 30 to an energy regime where they can be used to induce fusion evaporation reactions. PACE-2 calculations in combination with TRIM evaluations are able to theoretically evaluate the results of measurements and allow important conclusions such as the fact that these heavy species can be accelerated up to very high energies of around 5 MeV/A. Further theoretical and experimental improvements are necessary in order to obtain a better description of the reaction channels. This will finally lead to the technical exploitation of laser induced ion production the near future [1,2].
As in every new advanced technology there are a series of obstacles to be overcome in order to progress. The exact mechanism for the interaction of charged particles with intense electromagnetic fields has been considered for more than fifty years, but has remained unclear until today. The violent creation mechanism, the high fields that are produced by the electron plasma, the extremely short time spans and the variety of the processes involved are of such a complex nature that any qualitative and quantitative description is impossible to achieve at the moment. From the practical point of view these deficits hinder the full technological exploitation of the unique high power laser facilities.
Within this frameset the onset of laser induced fusion evaporation reactions leading to specific ion species has to be regarded as a crucial milestone, as it proves in principle the feasibility of the technological concepts mentioned above.
Recent developments in high intensity lasers open up a new approach to investigating nuclear reactions in the laboratory without access to nuclear reactors or particle accelerators. By focusing the laser spot, very high
laser intensities in excess of 1021W / cm2 can now be produced. Under these conditions, matter in the focal spot is turned into hot dense relativistic plasma with
temperatures of ten billion degrees ( 1010 K ) - temperatures comparable to those that occurred one second after the "big bang". The laser interactions with solid or gas targets can generate collimated beams of highly energetic electrons and ions. The possibility of accelerating electrons to energies over 200 MeV in such experiments led to the utilization of high-energy bremsstrahlung radiation in order to investigate laser-induced gamma reactions. Laser-induced activation, transmutation, fission and fusion have been demonstrated with both single pulse giant laser systems and laboratory tab-letop laser
systems.
With the help of modern compact high-intensity lasers, it is now possible to produce highly relativistic plasma in which nuclear reactions such as fusion, photonuclear reactions, and fission of nuclei have been demonstrated to occur. This new development opens the path to a variety of highly interesting applications, the realization of which requires continued investigation of fundamental processes by both
theory and experiment and in parallel the study of selected applications. The possibility of accelerating electrons in focused laser fields was first discussed by Feldman and Chiao in 1971. The mechanism of the interaction of charged particles in intense electromagnetic fields, for example, in the solar corona, had, however, been considered much earlier in astrophysics as the origin of cosmic rays. In this early work, it was shown that in a single pass across the diffraction limited
focus of a laser power of 1012W, the electron could gain 30 MeV, and become relativistic within an optical cycle [4].
Nuclear reactions induced by ultra intense lasers became amenable in the last couple of years by the evolution of experimental relativistic laser plasma physics. Laser systems like the JENA 15 TW tabletop Ti:sap-phire laser generate light intensities of up to
1020W / cm2 in their focal spot. The corresponding
electric field is 3 x 1011 V/ m, being a hundred times larger than the inner atomic fields. Matter, exposed to these extreme conditions, turns into a hot dense plasma in which electrons are accelerated by various
mechanisms to energies exceeding the electron rest mass energy by more than two orders of magnitude. These fast electrons can now be used for bremsstrahlung generation in high Z targets with photon energies as well reaching several tens of MeV.
Recent experiments have demonstrated that lasersolid interactions at intensities greater than
1019 W / cm2 can produce fast electron beams of several hundred MeV [7], several MeV y rays, up to 58 MeV proton beams [8], and heavier ions [9] of up to 7 MeV/nucleon.
The effects of radiation reaction (RR) have been studied extensively by using the interaction of ultraintense lasers with a counter-propagating relativistic electron. At the laser intensity at the order of
1023W / cm2 , the effects of RR are significant in a few laser periods for a relativistic electron. However, a laser at such intensity is tightly focused and the laser energy is usually assumed to be fixed. [10].
About Laser-initiated primary and secondary nuclear reactions in Boron-Nitride was reported in [18]
Induced transitions in collisions of ordinary [12] and exotic [13] atoms in the field of a strong electromagnetic wave have been discussed in [12,13]. It has been shown that processes that are forbidden or occur with low probability in collisions of free atoms or ions may have large cross sections in the presence of sufficiently intense laser radiation. In collision theory, such processes have come to be called "radiation collisions."
The mechanism of nuclear reactions is of course different from that of atomic collisions. But in this case, too, we may ask whether a strong electromagnetic field might not affect the cross sections for collisions of nuclear particles, e.g., for neutron-nucleus collisions. The radiative capture of a neutron by a nucleus is a well investigated nuclear reaction [14]. As a rule, however, this reaction is accompanied by the spontaneous emission of hard photons with energies of the order of 1 MeV or higher. The probability for the spontaneous
emission of optical quanta in the radiative capture of a neutron is low. Nevertheless, the induced capture of a neutron with transition of the neutron + nucleus system from the continuum to a weakly-bound compound-nucleus level (free-bound transitions) is possible in a sufficiently intense laser field [15]. The earlier estimates [15-17] of the cross sections for induced capture of a neutron by a nucleus, however, showed that not every level of the compound nucleus can be excited in the presence of an external laser field of moderate intensity. If the neutron width of the level corresponds to optical-model estimates, the laser power necessary for observing induced capture should be so high as to be achievable only in very short (10-9 sec) pulses.
Because of the Porter-Thomas fluctuations, the neutron widths of the compound-nucleus levels may actually differ substantially from the average values predicted by the optical model. The observed p levels of the compound nucleus in the region of neutron-resonance energies have anomalously large neutron widths. To clarify the actual possibility of observing induced excitation of p levels of the compound nucleus, therefore, it is necessary:
In the present paper we try
a) to generalize the theory to the case of an induced transition of the neutron +nucleus system from an s state of the continuum to a final p state of the compound nucleus that also lies in the continuum (free-free transitions); and
b) to estimate the intensity of the laser radiation necessary for observing the induced capture of a neutron by a nucleus for known p levels of the compound nucleus in the region of neutron-resonance energies (< 1 keV).
2. INDUCED TRANSITIONS OF THE NEUTRON +NUCLEUS SYSTEM IN THE CONTINUUM
In an external electromagnetic field, the neutron + nucleus system may undergo a transition from a continuum s state to ap state with the emission (or absorption) of a field quantum. As a result, the energy of the system must change by an amount equal to the energy fid) of a field quantum (~1 eV for the optical region), i.e., the neutron is scattered inelastically. If the energy of the final p state of the system is close enough to that of a compound-nucleus level whose neutron width is sufficiently large, then, other conditions being equal, the inelastic scattering cross section must increase. Let us examine this process in more detail.
In the dipole approximation, the potential for the interaction of the neutron + nucleus system with the external electromagnetic field has the form
V = -efVnE(vn, t), (1 )
where rn is the relative coordinate and E(rn, t)
is the strength of the electric component of the electromagnetic field
E = E0 cos(®t - krn). (2 )
We may use perturbation theory to find the cross section for inelastic scattering with transition of the neutron from an initial state of energy £ to a state of
energy Sp+hco. Then the cross section for inelastic
scattering of a neutron by a nucleus in the field of wave (2 ) can be written in the form
d°nP = frf £K\2S(spTha-E), (3 )
"0 '
where kQ = (2ms ) / /? is the wave vector of
the incident neutron, the sign £ indicates summation over the final states and
1
V01 =2 eeff (<0 E0r^l)
is the matrix element, (p0 and < being the initial-and final-state wave functions.
Voi = i2xeeffEo<o\KR)<i(kiR)R2. (4 ) (R is the nuclear radius),
The conditions k0R << 1 and kR << 1 are always satisfied for slow neutrons, and we may also assume that S01 << 1 where S0 is the s-wave phase
shift; hence, by expanding (4) in the appropriate way and neglecting potential scattering, we obtain an expression for the cross section in the form
da-p — 3 k 2
r r
np n
dil 4 (s+ha-EJ+T1 /4
where r is given by
cos2 0O, (5)
1 eeffE0
U
\2 r
rn -— ,
np 3 (tico)2 \tico
R
rn(ßp)112; (6)
v0 J
here £ is a dimensionless quantity (£ =£ /1
eV), and I and r are the elastic and reduced neutron widths, respectively, of the p resonance of the compound nucleus. On integrating (5) over the angles we obtain the usual formula for resonant neutron scattering:
a —
np
n
r r
np n
k2 (e ±ha>-En)2 +r2/4
(7 )
where I, I and En are the neutron elastic width, the total width, and the energy of the resonance, respectively, E1 is the neutron energy, and S t is the p-wave potential-scattering phase shift in which U(rn ) is the effective nuclear potential for the neutron dU
-= —U0S(rn — R),, where U0 is the depth of the
well.
It follows from Eq. (6) that I and therefore also
the cross section, is proportional to the power of the laser radiation. It should be emphasized that perturbation theory was used in deriving Eq. (7) and that I cannot
be arbitrary (I < I). If all the parameters (In, I,
En and S1) of the p level of the compound nucleus are
known, I can be estimated without difficulty. The
total width I of the compound-nucleus level is determined, as a rule, by neutron elastic-scattering and radiative- capture processes. For the heaviest nuclei, we must add fission to these processes, i.e., I = rn+r +If=In+y, where y is the width
of the compound-nucleus level for decay via the radiative and fission channels. Taking these remarks into account, we see that the cross section <Tc for induced nuclear reactions (fission and radiative capture) must have the form
n
ac —
r y
npi
k2 (E ±ha-En) +r /4
. (8 16)
By estimating I and knowing the width y of the given p level of the compound nucleus, we can evaluate Gc. The results of estimates for a number of compound-nucleus p levels are as follows. In all cases the depth of the potential-energy well was taken as
50 x106 eV, and the nuclear radius, R = 1.24A113 Fm . The corresponding experimental values were taken for the quantities a0 = S0 / k0, In, and I. The
case in which the scattering amplitude in the initial s state has a resonance associated with a level of the compound nucleus and there is also a corresponding level in the final p state is of interest. The compound nucleus
U239 has two such levels at 6.67 and 4.41 eV, respectively [7]. The energy separation ha) =2.26 eV between these levels falls within the energy range of optical quanta. Calculation shows the results of the cross section for induced capture of a neutron at the 6.67 and
4.41 eV resonances of U238 with the 6.67 - 4.41 eV transition (see [49-77]).
It is evident from the calculations that the cross-section ratio may turn out to be of the order of unity
2
when the intensity of the electric component of the electromagnetic field reaches the quite moderate value
E ~ 5 x103 V/crn.
3. CONCLUSION
The estimates presented above show that it is quite feasible to observe induced nuclear reactions. For this purpose one will need a laser that provides a radiation
flux of at least 104 W/cm 2 . A pulsed laser of that power should be pulsed in synchronism with a pulsed neutron source. When the laser is off the cross section for the nuclear reaction (radiative capture or fission) will be small. When a laser of the indicated power is on, and if the condition sp±hco& En is satisfied, the
nuclear reaction cross section should be appreciably larger and should increase linearly with increasing laser power. The target must contain enough atoms of the investigated isotope and must be transparent to the laser radiation. The necessary intensity of the laser radiation is far below the threshold for breakdown.
References
1. K. Spohr, R. Chapman, K. Ledingham, P. Mckenna, Rom. Journ. Phys., Vol. 50, Nos. 7-8, P. 651-655, Bucharest, 2005
2. K. Ledingham et al., J. Phys, D36 L79 (2003).
3. P. McKenna et al., Phys. Rev. Lett., 91 (7): art. no. 075006 (2003).
4. Joseph Magill, High-Intensity Lasers in Nuclear Science, Radiochemistry and Nuclear Chemistry
- Vol. II - High-Intensity Lasers in Nuclear Science 2005.
5. Strickland D and Mourou G, Opt. Comm. 56(3) 219 (1985)), Chirped Pulse Amplification (CPA) by Strickland and Mourou allowed intensities I
> 1015 W/cm2 .
6. F. Ewald, H. Schwoerer, R. Sauerbrey, J. Galy, J. Magill, R. Schenkel, Quantum Electronics 1. Laser Induced Nuclear Reactions, 2014.
7. Malka V et al Science, 2002, 298, 1596
8. Snavely RA et al, Phys. Rev. Lett 2000, 85,
2945
9. McKenna P et al, Phys. Rev. Lett 2003, 91,
10. J. F. Ong , T. Moritaka , and H. Takabe, Physics of Plasmas 25, 033113 (2018).
11. C. Labaune, C. Baccou, V. Yahia, C. Neuville & J. Rafelski, Scientific Reports 6, 21202 (2016) .
12. L.I. Gudzenko, L.A. Shelepin, S.I.Yakovlenko, Usp. Fiz. Nauk 114, 457 (1974).
13. D.F. Zaretskiy, V.V. Lomonosov, V.A. Lyul'ka, Zh. Eksp. Teor. Fie. 77, 867 (1979)
14. J. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics, Springer Verlag, 1977.
15. D. F. Zaretskii, V. V. Lomonosov, Pis'mav Zh. Eksp. Teor. Fiz. 30, 541 (1979).
16. D. F. Zaretskil and V. V. Lomonosov, Zh. Eksp. Teor. Fiz. 81,429 (1981).
17. E.A. Ayryan, A.H. Gevorgyan, I.V. Dovgan, K.B. Oganesyan, arXiv preprint arXiv:1902.07610.
18. Donald J . Hughes and Robert B. Schwartz, BNL-325, Brookhaven Nat'nl. Lab., 1958.
