aa r X i v : . [ nu c l - t h ] D ec Deuteron disintegration by reactor antineutrinos
L.M.Slad * Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow119991, Russia
The existence of a new interaction involving the electron neutrino and the nucleons, which hasreceived a convincing confirmation through a good agreement between the theoretical and experimentalresults concerning all observable processes with solar neutrinos, should also inevitably manifest itselfin the deuteron disintegration by reactor antineutrinos neutral currents. In this paper, the analyticaland numerical characteristics of such a disintegration are presented. The attention is drawn to theproblem of finding the neutron registration efficiency, discussed in the preparation of the experiment atthe Sudbury Neutrino Observatory and in a number of special studies, to the role of quenching gas inproportional counters with helium-3 and to three performed reactor experiments with heavy water.
1. Introduction
In the work [1], we have presented a substantiation of the existence of a hidden enoughnew, semi-weak, interaction involving at least the electron neutrino and the nucleons, which iscarried by an (almost) massless pseudoscalar boson ϕ ps . The electron does not possess such aninteraction at the tree level. We adhere to the classical concept that the neutrino field of anysort is described by a bispinor representation of the proper Lorenz group and obeys the Diracequation. The semi-weak interaction Lagrangian has the following form L = ig ν e ps ¯ ν e γ ν e ϕ ps + ig Nps ¯ pγ pϕ ps − ig Nps ¯ nγ nϕ ps . (1)The semi-weak interaction manifests itself clearly in the results of experiments with solarneutrinos due to the fact that the Sun essentially plays the role of part of the experimentalsetup, providing about 10 collisions with its nucleons for every neutrino. Each such a collision,firstly, changes the neutrino handedness, so that at the exit from the Sun the fluxes of left- andright-handed electron neutrinos are approximately equal, and, secondly, reduces the neutrinoenergy ω in proportion to its square: ∆ ω ≃ ω /M , where M is the nucleon mass. Having theonly free parameter, the effective number of neutrino collisions with the Sun nucleons n , orthe value of the product of the coupling constants g psν e g psN , we obtained a good agreementbetween the theoretical results based on Lagrangian (1) and the results of all the five typesof experiments with solar neutrinos: Cl → Ar, Ga → Ge, ν e e − → ν e e − , ν e D → e − pp ,and ν e D → ν e np . Such an agreement is reached at n = 11. On the basis of this number, thefollowing estimate is obtained g ν e ps g Nps π = (3 . ± . × − . (2)The results of the first four mentioned experiments reflect the semi-weak interaction ofthe electron neutrinos in the Sun. At the same time, the results of the experiment on thedeuteron disintegration by the solar neutrinos neutral currents reflect the semi-weak interactionof electron neutrinos, both in the Sun and in the terrestrial installation. Specifically, thedisintegration of the deuteron into a proton and a neutron is caused by two non-interferingsub-processes. In the first sub-process, which has a standard description based on the Weinberg-Salam model, only the left-handed solar neutrinos are involved that interact with the deuteron * [email protected] ucleons through the Z -boson exchange. Accurate calculations of the cross-section of thissub-process are given in works [2]–[4]. In the second sub-process caused by the semi-weakinteraction, both the left- and right-handed solar neutrinos are involved due to the masslesspseudoscalar boson exchange with the deuteron nucleons. The cross-section of this sub-process σ ps ( ω ) is calculated in work [1] within a long-standing practical approximation. It is given bythe formula σ ps ( ω ) = ( g ν e ps g Nps ) π M · (cid:18) M n − M p M (cid:19) · √ B ( √ B − ( a s √ M ) − ) ω × Z ω − B dE r ( ω − B − E r ) √ E r ( E r + B ) ( E r + ( a s M ) − ) , (3)where B = 2 . δ = M p − M n = − . a s M ) − = 0 . σ ps ( ω ) (3) are of two types, namely, the ones coming from an errorin the coupling constant product (2) and the other from the approximation in the calculationof this quantity. We estimate the latter error from the discrepancy between the cross-sectionvalues for the Z -boson exchange sub-process obtained by accurate computations in work [2],and the values obtained by a method analogous to our present approximation. This is reflectedin table 5 of the work [1], where the most significant difference is at the process threshold.
2. The rates of the deuteron disintegration by neutral andcharged currents of reactor antineutrinos, ¯ ν e D → ¯ ν e np and ¯ ν e D → e + nn Note, that at the energy values ω , typical for solar neutrinos and reactor antineutrinos, thecross-sections of the deuteron disintegration by neutrino and by antineutrino caused by the Z -boson exchange, σ ν e Z ( ω ) or σ ¯ ν e Z ( ω ), show only a minor difference [3]. The deuteron disintegrationcaused by the ϕ ps -boson exchange has identical cross-sections for neutrinos and antineutrinos.The numerical values of the cross-sections for the both sub-processes with reactor antineutrinosare given in table 1. Table 1.
The cross-sections of the deuterondisintegration σ ¯ ν e Z ( ω ) σ ps ( ω ) (in units of 10 − cm ). ω σ ¯ ν e Z ( ω ) σ ps ( ω ) ω σ ¯ ν e Z ( ω ) σ ps ( ω ) ω σ ¯ ν e Z ( ω ) σ ps ( ω )(MeV) [4] Eq. (3) (MeV) [4] Eq. (3) (MeV) [4] Eq. (3)2.2 0.0000 0.000 4.2 0.396 1.476 6.2 2.215 2.6462.4 0.0004 0.037 4.4 0.505 1.621 6.4 2.490 2.7342.6 0.0042 0.151 4.6 0.630 1.759 6.6 2.782 2.8182.8 0.0144 0.303 4.8 0.707 1.890 6.8 3.092 2.8993.0 0.0332 0.473 5.0 0.927 2.015 7.0 3.419 2.9763.2 0.0621 0.649 5.2 1.100 2.134 7.2 3.764 3.0503.4 0.1025 0.825 5.4 1.289 2.247 7.4 4.126 3.1203.6 0.1553 0.997 5.6 1.495 2.354 7.6 4.506 3.1883.8 0.2213 1.163 5.8 1.718 2.456 7.8 4.904 3.2534.0 0.3012 1.323 6.0 1.958 2.553 8.0 5.320 3.315In what follows, any quantity A related to reactor antineutrinos produced in the fission ofthe isotopes U, U, Pu, and
Pu will be denoted, respectively, as A , A , A , and A . Recall a number of known things. The energy released in the fission of any of the listed sotopes, E (in MeV/fission), is approximately the same: E = 201 . E = 205 . E = 210 . E = 213 . α ( t ) of the isotopes to thenumber of fissions in a reactor change with time. For example, during a standard operationperiod of a VVER-1000 reactor, they change in the intervals as follows [6]: α ( t ) ∈ [0 . , . α ( t ) ∈ [0 . , . α ( t ) ∈ [0 . , . α ( t ) ∈ [0 . , . S i ( ω ), i = 5 , , ,
1, discovered bythe collaboration Daya Bay [7] under comparing their experimental results with the results ofthe widely known works [8] and [9]. In our calculations, we use the results of work [8].The cross-sections of the deuteron disintegration by neutral currents integrated over thespectra of reactor antineutrinos per one fission of a considered isotope (named as the integralcross-sections), Σ Z ,i = Z B S i ( ω ) σ ¯ ν e Z ( ω ) dω, Σ ps ,i = Z B S i ( ω ) σ ps ( ω ) dω, (4)are presented in table 2 for both sub-processes, as well as their sums Σ Z+ps ,i = Σ Z ,i + Σ ps ,i .Values, presented for comparison in the last line of table 2, are the integral cross-sections ofthe deuteron disintegration by the reactor antineutrino charged current, calculated with usingthe σ ¯ ν e cc ( ω ) values taken from [2]. Table 2.
The integral cross-sectionsof the deuteron disintegration (in unit of10 − cm /fission). U U Pu PuΣ Z ,i ps ,i Z+ps ,i cc ,i r X ( t ) = α ( t )Σ X , + α ( t )Σ X , + α ( t )Σ X , + α ( t )Σ X , , (5)where X = Z , ps , Z + ps , cc, will be called the weighted integral cross-sections. During a stan-dard operation period of a VVER-1000 reactor, the weighted integral cross-sections changewithin the following intervals (in unit of 10 − cm /fission): Σ r Z ( t ) ∈ [0 . , . r ps ( t ) ∈ [0 . , . r Z+ps ( t ) ∈ [1 . , . r cc ( t ) ∈ [0 . , . ϕ ps exchange (in units of 10 − cm /fission):Σ r Z = 0 . · (1 ± . , Σ r ps = 0 . · (1 ± . · (1 ± . · (1 ± . . · (1 ± . , Σ r Z+ps = 1 . · (1 ± . · (1 ± . · (1 ± . . · (1 ± . , Σ r cc = 0 . · (1 ± . . (6) comparison of these cross-sections with those in table 2 for the pure uranium-235 reactorshows that the ratio between them is from 1.08 to 1.13. Since such a difference is not essentialfor our problem, then, in the future, we use the values of the cross-sections (6) without anyreservations.Take E = 205 MeV/fission as the energy released in the reactor at the fission of any isotope.Then, for an experimental installation filled with heavy water D O of mass m and placed atthe distance R from the reactor with thermal power W , the per day number of the deuterondisintegration events N X caused by this or that process or sub-process X can be calculated bythe following formula N X = 1 . · · Σ r X · W megawatt · m kg · πR · fissionday . (7) The new experiments on the deuteron disintegration by reactor antineutrinos, which I callfor in this paper, can play a very important role in confirming (or disproving) the hypothesisof the existence of a new interaction involving the electron neutrinos, if their results will haveapproximately the same level of reliability as the experiment on the deuteron disintegration bysolar neutrinos, carried out at the Sudbury Neutrino Observatory (SNO).At the SNO, three different techniques were used to register neutrons in events caused byneutral neutrino currents, ν e + D → ν e + n + p . In the first phase of this experiment [10],the neutrons were detected via capturing by deuterium, with the emission of gamma quantumwith the energy of 6.26 MeV. In the second phase [11], the NaCl salt was dissolved in heavywater and the neutron was detected by capturing it with the Cl nucleus emitting a cascadeof gamma quanta with total energy of 8.6 MeV. In the third phase, the neutron was registeredby proportional counters with He gas [12]. The registration of neutrons in the third phaseis much more complex case than in the first and second phases. Considerable preliminarystudies were devoted to the development of its methodology, some of which are presented in avoluminous article [13]. The absence of any noticeable defects in this technique is evidencedby the agreement between the results of all three phases of the SNO experiment.The deuteron disintegration by reactor antineutrinos have been studied in three performedexperiments. One such experiment took place in two stages at the Savannah River Plantreactor [14], [15], and another experiment with the same (or identical) installation, with thesame methodology and with a number of common participants took place at the Bugey reactor-5 [16]. The third experiment in two stages was carried out at the Rovno reactor [17], [18]. Inall these experiments, proportional counters with the He gas were used to register neutrons.The identification of events is complicated compared with the SNO experiments by the factthat, at the deuteron disintegration by reactor antineutrinos, neutrons are produced under theeffect of both the neutral and charged currents, ¯ ν e + D → ¯ ν e + n + p and ¯ ν e + D → e + + n + n .Published reports about each of these experiments contain some mystery, unexplainedelements. We shall note some of them only so that the preparation for setting new experimentson the deuteron disintegration by reactor antineutrinos, if they will take place, was conductedat a much higher level than in the performed experiments. Below we will pay attention, firstly,to different aspects of the problem of finding the efficiency of neutron registration by helium-3counters, which have been discussed at the preparation of the SNO experiment and in a numberof special studies carried out after 2000, and, secondly, to the problem of preventing spuriouspulses in the proportional counters, solved at the SNO.At the SNO, the efficiency of neutron registration by He-counters of the installation wasdetermined by various methods described in detail in the article [19]. One method is based onthe uniformly distributed introduction into a ball with heavy water of the Na isotope with a alf-life of 14.96 hours, emitting gamma rays, some of which has caused the disintegration ofdeuterons and the appearance of neutrons. It has gave to the neutron registration efficiencythe value equal to 0 . ± . Cf- and AmBe-neutronsources at different points of the D O volume using a manipulator. This method did not playan independent role, but was used to tune Monte Carlo calculations, which have establishedthe efficiency value equal to 0 . ± . He andCF in the ratio of 85% and 15% (by pressure) at 2.5 atm [19]. CF acts as a quenching gas,which preventes spurious pulses in the counters [13].In the work [16], the counters are filledwith a mixture of He and Ar with partial pressures of 1 and 1.7 atm, respectively. In the work[18], the He-gas pressure is 4 atm. In experiments [15], [16], and [18], there seems to be noquenching gas in the proportional counters.In the meantime, I note a few facts concerning the neutron capture process n + He → p + H.The dependence of the cross-section of this process σ on the kinetic energy E neutron is givenby the following relation [20]: σ = (847 . ± . E/ eV) − / b, if E <
11 eV . (8)From here, at the thermal energy of E = 0 . o C,one obtains that σ = 5300 b. When partial pressure of He gas is equal to 1 atm, the pathlength of the neutron until its capture is approximately 7.0 cm, and, at a pressure of 2.1 atm(as at the SNO), it is approximately equal to 3.3 cm. Meanwhile, the diameters of the counterswith He in works [15], [16], and [19] are the same and equal to 5.08 cm. The neutron, oncein a proportional counter, can make there Brownian motion upto the capture by the helium-3,but can also with high probability due to its Brownian motion go beyond the counter backinto heavy water. The compiler of the Monte Carlo program should take into account, if hecan, this circumstance in calculating the efficiency of neutron registration. Without taking intoaccount the possibility of neutron output from a counter, the Monte Carlo program will givean increased value of efficiency.In the works [21] and [22], an experimental study of the efficiency of neutron registration by aseparate He-counter at well-defined locations of AmLi- and
Cf-neutron sources, respectively,was carried out. In the work [21], the dependence of the relative efficiency on the partial pressureof the He gas in the range from 2 to 10 atm is found. In particular, when the pressure decreasesfrom 4 to 2 atm, the efficiency decreases by about 1.4 times. In the work [22] the dependenceof the absolute efficiency on the partial pressure in the range from 1.0 to 3.0 atm, at which itincreases by 1.55 times, from 0.076 to 0.118, is given.In the studies [21] and [22], CO is used as a quenching gas in the He-counters.
4. A view of the performed experiments on the deuterondisintegration by reactor antineutrinos
Let us consider now the lessons taken from three experiments on the deuteron disintegrationby reactor antineutrinos [15], [16], and [18]. In the Savannah River Plant experiment, thethermal power of the reactor was considered to be W = 2000 megawatt, the experimentalinstallation was at a distance of R = 11 . m = 268 kg. In the Bugey experiment [16], they were respectively: W = 2785 megawatts, R = 18 . m = 267 kg. For the Rovno experiment [18], ones consider that W = 1375 ± W = 1195 MW), R = 18 . ± . m = 2985 ± h η i and for double-neutron events (cid:10) η (cid:11) are considered equal to 0 . ± .
02 and 0 . ± . (cid:10) η (cid:11) and h η i differ a little enough. The method of findingthese efficiencies is not specified. The weighted average number of all events detected per daywith one and two neutrons are R n = 68 . ± . R n = 3 . ± .
83, respectively.The main objective of the experiment [15] was to find the value of R = CCD exp / NCD exp
CCD th / NCD th , (9)where CCD (NCD) is the rate of the deuteron disintegration process by a charged (neutral)current of reactor antineutrinos. A few years later, Reines admitted [23] that the intention ofthe experiment ”is based on the fact that the charged current should reflect the presence ofan oscillation, if it is in the detectable region.” It would seem that the hope on the oscillationdetection has became true, because it has been announced [15] that R = 0 . ± .
21, or0 . ± .
22 depending on the theoretical spectrum of reactor antineutrinos. This result wasperceived by the scientific community just as an indication of neutrino oscillations (see, forexample, [24], section 29).It’s been almost 20 years. In a number of experiments with reactor antineutrinos, theirsignificant oscillations were not revealed. In agreement with this, the work on the deuterondisintegration at the Bugey reactor [16] has gave the value R = 0 . ± .
23 for the ratio (9).The initial value of the single neutron registration efficiency, found by periodically placingthe neutron source
Cf in the center of the detector target, was h η i = 0 . ± .
01. Thesubsequent startup of the Monte Carlo program has gave the value h η i = 0 . ± .
01. It wasconsidered that (cid:10) η (cid:11) = h η i . At the same time, in table III of the article [16] there is anundefined ”software efficiency” , which is considered equal to 0 . ± .
003 (0 . ± . , was respectively R n = 19 . ± . R n = 1 . ± . η was calculated by placing sources Sb-Be and
Pu-Li (for which thecalibration problem is not discussed) in a large number of heavy water points, by finding theregistration probability of the neutron, produced in each of these points and by subsequentaveraging over them. The result is that h η i = 0 . ± .
010 and (cid:10) η (cid:11) = 0 . ± . (cid:10) η (cid:11) and h η i , 0 . ± .
012 versus 0 . ± . R n = 275 ±
31 and R n = 59 ±
7, respectively. Compared to the results at theSavannah Rive and Bugey reactors, the reactor in Rovno has a very high portion of registeredevents with two neutrons, namely: R n /R n is equal to 0 . ± .
038 in [15], 0 . ± .
011 in[16] and 0 . ± .
050 in [18]. This situation seems to us to be the most significant summaryresult of all three experiments discussed.Note that the ratio R n /R n does not depend on the reactor power, on the distance betweenthe plant and the reactor, on the amount of heavy water, and that the declared values of theefficiency of registration of single neutrons in all three experiments are close to each other.Therefore, it is justified to assume that the absence of quenching gas in proportional counterswith helium-3 leads to spurious pulses, and that part of the events with one neutron is registeredas events with two neutrons. It is quite possible that the portion of spurious double-neutronevents depends on all characteristics of proportional counters in their operating state, and thatthis portion is much higher in the experiment [18] than in the experiments [15] and [16]. Thespirious pulses, of course, also lead to an overestimation of the neutron registration efficience,found by means of radioactive sources of neutrons. here is no doubt that in the absence of a noticeable manifestation of antineutrino oscilla-tions in experiments near a reactor, if they exist at all, the real rate of deuteron disintegrationcaused by the charged current of the reactor antineutrinos must coincide with the theoreticalvalue N cc . Then the equality R n = D η E N cc (10)can serve as a check of the otherwise found efficiency of registration of events with two neu-trons (cid:10) η (cid:11) . The experimental rate of deuteron disintegration by neutral currents of reactorantineutrinos R nc is given by the following equation R nc = R n + 2 R n h η i − N cc . (11)Note that all three performed experiments on deuteron disintegration by reactor antineu-trinos are valuable above all by lessons which we can take when comparing their results witheach other.
4. Conclusion
Setting accurate experiments on the deuteron disintegration by reactor antineutrino isextremely challenging. The preparation and carrying out such experiments should be basedon the extensive and diverse methodological and practical base of the SNO, developed andwell-proven in setting experiments with solar neutrinos, as well as on new studies of variousaspects of neutron registration by proportional counters with helium-3.I am sincerely grateful to S.P. Baranov for the discussion of problems connected with thepresent work.
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