Absorption of Solar Neutrinos in Deuterium

Abstract

The nuclear reactions occurring in the solar interior which are thought to be responsible for solar energy production 1 may be verified directly, by observing the neutrinos created in the over-all reaction in the cycle (1) Bahcall 2 has obtained a theoretical spectrum of solar neutrinos, and has suggested the initiation of an experimental program of solar neutrino spectroscopy, based upon an observation of neutrino-induced nuclear reactions with various thresholds. Such a program would also check on details of solar models used in the calculation of the neutrino fluxes and provide a measure for the temperature at the sun's center. Most efficient for inducing nuclear reactions would be the neutrinos from the step B 8_ Be 8* + e+ + l (2) of the p-p cycle, because of their high energy (end point at 14.1 MeV). 3 So far, only experimental upper limits on solar-neutrino fluxes have been set; 4 positive results are expected shortly from two experiments now in progress. 5 ' 6 The experiment of Jenkins 6 proposes to detect the solar neutrinos in the reaction v +H 2 -2H 1 +e~, eby observation of the Cerenkov radiation of the electrons in a 2000-liter heavy-water target. The cross section and the electron spectrum and angular distribution of Reaction (3) are obtained theoretically in the following. 7 The conclusion is that the Coulomb repulsion will reduce the cross section only by an insignificant amount, so that solar-neutrino detection via (3) appears feasible.Calling v = neutrino momentum, T e (E e ) = electron kinetic (total) energy, p e -electron momentum, p = two-proton relative momentum, mp= proton mass, the kinematics of (3) gives v = Q + T +{p 2 /m ) e p (4)with a threshold of Q = 1.44 MeV. We use the conventional nonrelativistic weak-interaction Hamiltonian Gy + G^a^a^, where Gj± = -1.20Gy and Gy-\Q~~*mp~" 2 , and obtain the differential cross section da=2-2 Ti-3 G A l/l 2 A x (l-i?-p /vE )mbdQ p E dE dto ;3 *e e p y p^e e e e'it is isotropic in p, thus dQ,p = 2iT (identical particles), and shows a backward electron angular distribution. The following assumptions were made 7 : (1) The electron is treated as a free particle (as justified by its generally high energy).(2) The two protons emerge in a X S state; thus only the Gamow-Teller matrix element enters.(3) Retardation is neglected.(4) The effective-range approximation is used. 8 ' 9 Then the matrix element / containing the wave functions u^, U<IH of the relative motion (with the two-proton wave function normalized to 2) becomes6a) a (2//>) exp[*(a + 6)]ATsin6fj-(r s +rJ/4C I (6b) where 9 ' 10 4TT^2 = 150 MeV, C 0 2 = 277rj(e 2 ' 7? ?-1)-1 , r} = (2pR)-1 , fl = 2.88xl0~1 2 cm, and (see Preston 10 ) C 2 p cotd+R-Mv) = ~« s -1 + \ r s P Z > a =-7.72xl0-13 cm, r =2.72x10-" cm, s ' s (7) r f = 1.71xl0 -13 cm, and J= L°°e yr [G 0 (pr) +F 0 (pr) cot6]dr;145

Tests of electron flavor conservation with the Sudbury Neutrino Observatory

“…Therefore, we expect that the details of deuteron nuclear physics will play only a minor role. This expectation is confirmed by comparing the s-wave calculations performed in the 1960's by Kelly andÜberall [29] and by Ellis and Bahcall [30] using Bethe's effective range approximation [31] with the recent sophisticated calculations by Ying, Haxton, and Henley [32] and by Kubodera and collaborators [33,27]. The recent calculations include higher partial waves, relativistic effects, forbidden matrix elements, and exchange-currents.…”

“…The final state in the charged current reaction cannot be approximated by a pure two-body state. Even as early as the seminal Kelly-Überall calculation [29], it was noted that the attractive 1 S p-p interaction is not sufficient to bind the protons as an effective single particle, because of the presence of the repulsive Coulomb force. The two-body approximation would be equivalent to omitting the third and fourth terms in Eq.…”

Radiative corrections in neutrino-deuterium disintegration

“…Since radiative corrections are only few percent in magnitude, we follow Towner [6] and use for the 'tree level' differential cross section the formula based on the effective range theory (see [10,11]…”

Towards a model independent treatment of future solar neutrino data

“…where X NC νd , Σ ES , and X ES νµe are given in Eqs. (12), (20) and (21), respectively, r νd (E) = σ NC νd (E)/σ NC νd (E), rν ee (E) = σ νµe (E)/σν ee (E), rν µe (E) = σ νµe (E)/σν µe (E) and φν ℓ are the fluxes of antineutrinosν ℓ , with ℓ = e, µ, τ . In SNO and other future solar neutrino experiments it is planned to search forν e from the sun through the observation of the reactionν e p → e + n. Therefore, with the help of Eq.…”