- Email: [email protected]
Production of polarized neutrons by magnetic bremsstrahlung γ-rays
29 May 1997
PHYSICS
ELSETIER
LEl-fERS
B
Physics Letters B 401 (1997) 224-228
Production of polarized neutrons by magnetic bremsstrahlung y-rays I.P. Eremeev a, A.L. Barabanov b,l a International Business Nucleonic, Moscow, Russia h The Kurchatov Institute, 123182 Moscow, Russia Received 8 August
1996; revised manuscript
received 25 March 1997
Editor: R.H. Siemssen
Abstract Circularly polarized magnetic bremsstrahlung (“synchrotron”) y-radiation of ultrarelativistic electrons is suggested to be used to produce polarized pulsed neutrons by photonuclear reactions on light nuclei with a single valence neutron in
the p-shell. The polarization, spectral and integral characteristics of photoneutrons have been determined by multigroup calculations for ‘Be that is distinguished by an anomalously low neutron binding energy. @ 1997 Published by Elsevier Science B.V. PAC.? 25.20.-x;
29.25.D~ radiation;
Keywords: Synchrotron
Photonuclear
reactions;
Polarized
For years leading research centres have been searching for new methods of producing elementary particle beams by high energy accelerators. The increased energy of present day electron accelerators up to E N 50-100 GeV, on the one hand, and the advanced insertion devices with a spatial periodic magnetic field, on the other, open up possibilities to use magnetic bremsstrahlung (“synchrotron”, “undulatory’) radiation for these purposes. The use of magnetic bremsstrahlung (MB) radiation of ultrarelativistic electrons to produce neutrons through photonuclear reactions was proposed for the first time in Ref. [ l] and was discussed in Refs. [241. Below the principles of Ref. [ l] are extended to the production of polarized neutrons.
’ E-mail: [email protected]. 0370.2693/97/$17.00 0 1997 Published PIi SO370-2693(97)00418-S
neutrons
The approach is based on producing neutrons by circularly polarized MB y-radiation from ultrarelativistic electrons in a spatially periodic magnetic field of the form H=HX~cosF
+ZI.fisinF
(1)
with a period ho and different amplitudes of the horizontal H,,o and the vertical H$ components. The trajectory of electrons in such a magnetic field represents a deformed helix with its semiaxes proportional to H,o and H~o, respectively. The polarization of the MB yquanta depends on these components: the y-quanta are linearly polarized in the xz plane at HXo = 0 and circularly polarized along the z axis, when HXo = HYo. The specific features and the advantages of the proposed approach are due to a set of the MB properties, such as:
by Elsevier Science B.V. All rights reserved.
I.P. Eremeev, AL.. Barabanov
/ Physics Letters B 401 (1997) 224-228
(a) its high space-time and spectral density resulting from the high energy, large average current, ultrashort bunches and very small cross-section of electron beams in the modem accelerators; (b) the specific shape of the MB spectrum exponentially sloping in the higher energy region and the rather low energies of the quanta in the basic part of the spectrum; (c) the high degree of linear or circular polarization of the MB radiation; (d) the possibility of producing quasi-monochromatic y-quanta and neutrons, if the undulator radiation is used. Properties (a) and (b) provide the high spacetime and spectral densities of photoneutrons produced, whiIe (c) allows those to be polarized when the MB radiation is circularly polarized. In the case of an undulator magnetic field, when the values of the horizontal and vertical divergences of MB differ insignificantly, the geometry of the neutron production region would be considered approximately to be axially symmetrical. Because the MB divergence is very small, the radial dimension of the region is bound to be much less than the longitudinal one determined by the path length of y-quanta in the target. Such an axially symmetrical source with a high generation density has been labelled in Ref. [ 1] a “neutron focus”. Radically new properties exist to produce lowenergy neutrons without slowing down and polarized neutrons without polarizing. For the first purpose light nuclei with an anomalously low neutron binding energy, such as 9Be and D, should be used as a target [ 11. These nuclei are characterized by not only minimum values of the (7, n) reaction threshold, 1.665 and 2.225 MeV, respectively, but also by an abrupt growth of the reaction cross-section near the threshold. The latter dictates the specific shape of the photoneutron spectrum with a high density in the low-energy range. Nuclei with a single valence neutron in the p-shell, such as 9Be and i3C, are best suited to be a target to produce low-energy polarized neutrons. Their photodesintegration proceeds dominantly via an Eltransition with the emission of neutrons from the pJ bound state to the s-wave continuum, while the residual nucleus remains in its ground state O+. The total angular momentum of the valence neutron is J = 3/2 for 9Be and J = l/2 for i3C, coinciding with the spin
225
of a target nucleus. The ( y,n) threshold was specified above for 9Be and it is equal to 4.946 MeV for 13C. The wave function of a valence neutron in a p-shell bound state with total angular momentum J and a zero spin residual nucleus can be written in the form
is the spinor, describing the neutron state Here + with the projection u of the l/2 spin on an axis z, directed along the MB beam; Y,,(L), 4) is the sperical harmonic and C$@ are the Clebsh-Gordan coefficients, The amplitudes &+,(I), where M is a projection of spin J on an axis z, specify the initial spin state of the target nucleus. The probabilities ]a~( J) I2 do not depend on M when the target nuclei are nonpolarized. An absorption of a right/left polarized MB quantum in the case of a El-process leads to an increase/decrease in the orbital momentum projection m by unity, while the spin projection IT remains unchanged. As the projection m in the s-wave final state is zero, the amplitude u,” ( l/2) of the s-wave neutron final state with the projection u of the l/2 spin on the MB beam axis is determined by the product &l/2)
N uM(J)C;&
(3)
for right/left polarized MB radiation. We see that only the target nuclei with projection M = (+ F 1 participate in the El photodesintegration process induced by right/left polarized MB radiation leading to the production of the s-wave neutrons with projection cr. Note, that the angular distribution of the s-wave photoneutrons is isotropic, so the amplituoes a,( l/2) do not depend on the direction of the neutron emission. For a non-polarized target the neutron polarization equals (a) = *11-43(5+ Pn = 1/2 8
1) ’
(4)
where (a) =Ccrla,f(l/2)12 ,&l/:),2
N (c$/J’.U
I
Cl&l/2)12,
(5)
It follows that in the case of the right polarized MB radiation p,, = -0.5 for 9Be and pn = 1 for 13C. Pho-
I.P. Eremeev, A.L. Barabunov/ Physic& Letters B 401 (1997) 224-228
226
toneutrons emitted are polarized along the MB beam axis independently of the direction of their emission. In the general case of a direct El-transition from a p-shell state to the final state with orbital momentum I and total angular momentum j of the neutron with respect to the zero spin residual nucleus we get for the polarization averaged over all angles of emission Pn =
(3/4+j(j+I)-1(1+1))(2+j(j+l)-J(J+l)) Y(j+
1) (6)
In reality, 1 equals to 0 or 2 for a El-transition from a p-shell state, while the parity of the final state should be opposite to that of the initial state. If 1 = 0 and j = l/2 we return to the above result for s-wave final neutrons. The spectral density of photoneutrons produced in a target by the MB radiation formed by the single passage of an electron through a spatially periodic magnetic field is determined by the expressions
At E = 50 GeV mentioned above and ha = 5-6 cm, that is, at as small period as technically possible, the energy range of practical interest, namely E > 1.5 MeV, could be attained only when the higher harmonics of the radiation spectrum with k > 35 are used. It is fairly difficult to calculate the spectral angular characteristics of the undulator elliptically polarized radiation for the required great number of harmonics (about 200). Thus, we have restricted our consideration by an asymptotic case of a wiggler to estimate the spectral and integral intensity of polarized y-quanta according to the results of Ref. [ 51. The spectral density of the elliptically polarized yquanta emitted by an electron in a direction 0, = 0 in a wiggler with a number of periods NO was determined from the expression 8e2 NO E, N,I(E,)
x = f+,
Nrll(&)
x *
[1 - exp ( -Z,L)] Y
E
n
(Ey)
=A-* ACE,
,
Y
- E,n),
(8)
where NY1 is the spectral density of MB y-quanta per electron; A is the mass of the target nucleus; Er, E,, and Ey,, are the energies of the y-quantum, photoneutron and the (y, n) reaction threshold, respectively; a,( E,) and rry,,( E,) are the total cross-section and the cross-section of the (y, n) reaction for y-quanta of energy E,, respectively; X, is the macroscopic crosssection of attenuation for y-quanta in a target of length L along the MB beam. The energy of y-quanta emitted by an electron in the field ( 1) is determined by the expression
(9) where Afl = Aa/2y2, y = E/mc2, KxcY) = eH,o(,qAo/ 2n-mc2, k is the radiation harmonic number, 0, is the angle between the y-quantum emission direction and the z axis. Emitted at the angle 0, = 0 are only the odd harmonics and only the first one when H.,Q= HYo.
-
hcG--
c
Fx(Kx, z)
C
JG
+ F;(K,,
;)
c1,
(10)
where E,Q = he/h@, EC = (3/4r)eA,,HYoy2 is the “critical” energy of the MB spectrum, Ace is the Compton wavelength of an electron, the functions F, and FY are defined in Ref. [ 51. The degree of the circular polarization of emitted y-quanta was determined as Qy(fGt
Ey)
= 2JFx(Kx,EyIEC)FY(Kx,Ey/~,) fi(Kx,E,IE,)
+ &(K,,
E,/E,)
(11) ’
The photoneutron spectrum has been calculated at E = 50 GeV for a ‘Be target and the circularly polarized MB radiation from a wiggler with a length Lo = Naha = 900 cm, a period Aa = 12 cm, H>o = 2.3 T and K, = 1. The chosen values for E and H,o correspond to EC = 4.0 MeV. The value of K, = 1 has been chosen because a compromise has to be reached between the MB intensity and the degree of its polarization. The photoneutron spectrum provided by the linearly polarized MB radiation (K, = 0) has been calculated for comparison. The spectra normalized to a single passage of one electron through a wiggler are shown in Fig. 1. Nonpolarized neutrons are produced by linearly polarized y-quanta. The data [ 61 of the precision measurements
I.P. Eremeev. A.L. Barabanov /Physics Letters B 401 (1997) 224-228
227
Table 1 The characteristics of photoneutrons
N,, x IO6 , n/keVlel
.-.
MB polarization
Linear
Circular
QY
0 36 0 0.20
0.9 17 0.45-0.65 0.05
&I, de1 Ptl N,,!, n/e1
,
10
. * ..*..
1
*
100
I
1000
.
.
..I
\J
10000
E, , keV Fig. 1. The spectra of polarized (solid curve) and non-polarized (dashed curve) photoneutrons produced in the 9Be target by circularly and linearly polarized MB y-rays, respectively.
of the (y, n) cross-sections for Be were used for the calculation. The spectrum exhibits a high density of neutrons in the resonance energy range. The extrapolation of the results of Ref. [6] to zero shows that a spectral density of neutrons in the region below E, - E,, = 0.5 keV should be rather high due to the recoil of nuclei emitting photoneutrons. The kinematic corrections to the neutron energy E,, for emission angles of more than 90” for Be amount to 200400 eV to be sufficient to shift the zero of the E,, scale to the region of the noticeable values of gy,n in the E, - E,, scale.
According to Ref. [ 71 the total cross section of the 9Be( n, y)8Be reaction is determined mainly by a direct El-transition of neutron from ps/2-shell to continuum si/2- and d3/2-, dsl2-states for the energies Ey < 10 MeV. So only the l/2+, 3/2+ and 5/2+ excited states of the 9Be nucleus are significant. The contributions of the l/2- and 5/2- low-lying excited states of the 9Be, populated by E2 and Ml transitions, to the photoneutron spectra are small and may be neglected. The low-energy region of the spectra in Fig. 1 results from the emission of the s1/z-wave neutron (1 = 0, j= l/2), whiIe the next part of those is due to the dslz-wave (1 = 2, j = 512). So we can use the above described formalism to estimate the neutron polarization for these two parts of the spectrum. The magnitudes of the neutron polarization calculated by Eq. (6) for fully circularly polarized MB y-quanta are equal to pn = -0.5 and p,, = 0.7, respectively. Taking into account that the polarization of emitted y-quanta for the chosen wiggler parameters equals QY N 0.9, we
get the values of the neutron polarization P, = pnQy, shown in Fig. I. The third bump of the photoneutron spectrum, presented in Fig. 1, results from two different processes (see Ref. [ 71) . On the one hand, d3p- and ds/n-wave neutrons are emitted, and the residual *Be nucleus remains in its ground state Of. On the other hand, for E, 2 4.6 MeV a new channel of the reaction arises, corresponding to the sr/2-wave neutron emission while the *Be remains in its first excited state 2+. Note that in the latter process the total angular momentum J of the n+8Be system equals 3/2 or 5/2. Thus an estimate of the neutron polarization is difficult as not only the different weights of the listed contributions but also their interference should be properly accounted for. The calculation of the neutron polarization may be performed in the framework of some model of the reaction. However, the result will be model dependent. Therefore it would be more reasonable to determine the neutron polarization in this part of spectrum experimentally. For this reason we do not consider here the neutron polarization in the third bump. The integral characteristics expected have been calculated for the above conditions by integration over the ‘y-rays and neutron spectra. The results obtained are listed in Table 1. The table symbols are as follows: Q, is the degree of MB circular polarization; N,i is the total number of y-quanta emitted in the energy range E, 2 1.5 MeV by an electron in its single passage through the wiggler; P, = pnQr is the degree of the neutron polarization; N,I is the yield of photoneutrons per electron passage through the wiggler. The region length of the neutron production in the Be target is taken to be equal L N l/X,( E,) . If the magnitudes of E and H,o are increased to 70 GeV and 4.5-5 T, respectively, to correspond to a value of EC 21 15-17 MeV, the integral yield N,,t could be raised to 0.3 n/e1 for polarized neutrons and 1.0 n/e1 for non-polarized ones. For this reason the values
228
I.P. Eremeev, A.L. Barabanov/ Physics Letters B 401 (1997) 224-228
given in Table 1 should be considered as a lower limit for the possible values of the produced photoneutrons. It is evident from the data presented that the proposed approach has considerable promise for the use in fundamental investigations. This results from their characteristics such as: - a large pulsed neutron intensity and flux in combination with an ultrashort duration; - a possibility to produce polarized neutrons and to vary simply the degree and direction of their polarization; - a specific shape of the spectrum with a great density in the energy range of resonance neutrons; - a possibility to change simply the spectral end point in the wide energy region; - a minimum radiation loading the target and na radionucfides as compared with the other known methods of the neutron production. The corresponding source of polarized neutrons could be best realized on modern storage rings with an electron energy E 2 30 GeV and average current > 10 mA, such as LEP or HERA, whose beam parameters (see [2] and [ 81, respectively) allow the time average and peak flux of the polarized neutrons on a 9Be target surface to amount to N 10’6-10’7 n/cm*.s and - 5 . 10i9-5. 10” n/cm*+, respectively, at a neutron pulse duration determined as rll = L/c N 5. lo-‘O s. We note for comparison that at the best of the modern pulsed neutron sources, such as LANSCE and ISIS spallation sources, the average and peak flux of non-polarized fast neutrons on a surface of 238U,W or Ta targets are equal to N 5. 10’3-2. 1014n/cm*+ and N 1018-5 . 1018 n/cm*.s, respectively [9,10]. To produce slow polarized neutrons one uses Hz0 moderator and proton polarizer resulting in a neutron loss. Indeed, a fraction of fast neutrons incident to the surface of rectangular Hz0 moderators placed near
the targets amounts to 0.05-0.1 of the total number of produced neutrons. Transmission through a proton polarizer usually used to provide a degree of the neutron polarization near to the presented above in Table 1 does not exceed 0.2. Therefore, only a part of - lo-* of the total flux of the fast neutrons from the target can be used to produce slow polarized neutrons at the above spallation sources. The detailed calculation of the averaged and pulsed parameters for the proposed source in the case of both polarized and non-polarized neutrons and their comparison with the parameters of modern neutron sources is of special interest and will be carried out in a following paper. We are grateful to D.I? Grechukhin and D.F. Zaretsky taking interest in the problem. We thank the referee drawing our attention to the Ref. [3], unfortunately, being unavailable for us. References
[ I 1 II? Eremeev, JETP Lett 27 ( 1978) 10. [2] A. Hofmann, Phys. Rep. 64 ( 1980) 253. [3] G.C. Baldwin, Report LA-9051 (1981). [4] 1.P Eremeev, in: Proc. of the 1995 Particle Accelerator Conference and International Conference on High Energy Accelerators (Dallas, May 1995), Vol. I, p. 146 (1996). [S] H. Kitamura, Synchrotron Radiation News 5 ( 1992) 14. [6] B.L. Berman, R.L. Van Hemert, CD. Bowman, Phys. Rev. 163 (1967) 958. 171 T. Aurdal, 2. Naturforschung 24a ( 1969) I 188. IS] R. Brinkmann, in: Proc. of the 1995 Particle Accelerator Conference and International Conference on High Energy Accelerators (Dallas, May 1995). Vol. 1, p. 406 (1996). [9] PW. Lisowski, C.D. Bowman, G.J. Russell. S.A. Wender, Nucl. Sci. Eng. 106 (1990) 208. [IO] C.C. Wilson, Neutron News 6 (1995) 27.
PHYSICS
ELSETIER
LEl-fERS
B
Physics Letters B 401 (1997) 224-228
Production of polarized neutrons by magnetic bremsstrahlung y-rays I.P. Eremeev a, A.L. Barabanov b,l a International Business Nucleonic, Moscow, Russia h The Kurchatov Institute, 123182 Moscow, Russia Received 8 August
1996; revised manuscript
received 25 March 1997
Editor: R.H. Siemssen
Abstract Circularly polarized magnetic bremsstrahlung (“synchrotron”) y-radiation of ultrarelativistic electrons is suggested to be used to produce polarized pulsed neutrons by photonuclear reactions on light nuclei with a single valence neutron in
the p-shell. The polarization, spectral and integral characteristics of photoneutrons have been determined by multigroup calculations for ‘Be that is distinguished by an anomalously low neutron binding energy. @ 1997 Published by Elsevier Science B.V. PAC.? 25.20.-x;
29.25.D~ radiation;
Keywords: Synchrotron
Photonuclear
reactions;
Polarized
For years leading research centres have been searching for new methods of producing elementary particle beams by high energy accelerators. The increased energy of present day electron accelerators up to E N 50-100 GeV, on the one hand, and the advanced insertion devices with a spatial periodic magnetic field, on the other, open up possibilities to use magnetic bremsstrahlung (“synchrotron”, “undulatory’) radiation for these purposes. The use of magnetic bremsstrahlung (MB) radiation of ultrarelativistic electrons to produce neutrons through photonuclear reactions was proposed for the first time in Ref. [ l] and was discussed in Refs. [241. Below the principles of Ref. [ l] are extended to the production of polarized neutrons.
’ E-mail: [email protected]. 0370.2693/97/$17.00 0 1997 Published PIi SO370-2693(97)00418-S
neutrons
The approach is based on producing neutrons by circularly polarized MB y-radiation from ultrarelativistic electrons in a spatially periodic magnetic field of the form H=HX~cosF
+ZI.fisinF
(1)
with a period ho and different amplitudes of the horizontal H,,o and the vertical H$ components. The trajectory of electrons in such a magnetic field represents a deformed helix with its semiaxes proportional to H,o and H~o, respectively. The polarization of the MB yquanta depends on these components: the y-quanta are linearly polarized in the xz plane at HXo = 0 and circularly polarized along the z axis, when HXo = HYo. The specific features and the advantages of the proposed approach are due to a set of the MB properties, such as:
by Elsevier Science B.V. All rights reserved.
I.P. Eremeev, AL.. Barabanov
/ Physics Letters B 401 (1997) 224-228
(a) its high space-time and spectral density resulting from the high energy, large average current, ultrashort bunches and very small cross-section of electron beams in the modem accelerators; (b) the specific shape of the MB spectrum exponentially sloping in the higher energy region and the rather low energies of the quanta in the basic part of the spectrum; (c) the high degree of linear or circular polarization of the MB radiation; (d) the possibility of producing quasi-monochromatic y-quanta and neutrons, if the undulator radiation is used. Properties (a) and (b) provide the high spacetime and spectral densities of photoneutrons produced, whiIe (c) allows those to be polarized when the MB radiation is circularly polarized. In the case of an undulator magnetic field, when the values of the horizontal and vertical divergences of MB differ insignificantly, the geometry of the neutron production region would be considered approximately to be axially symmetrical. Because the MB divergence is very small, the radial dimension of the region is bound to be much less than the longitudinal one determined by the path length of y-quanta in the target. Such an axially symmetrical source with a high generation density has been labelled in Ref. [ 1] a “neutron focus”. Radically new properties exist to produce lowenergy neutrons without slowing down and polarized neutrons without polarizing. For the first purpose light nuclei with an anomalously low neutron binding energy, such as 9Be and D, should be used as a target [ 11. These nuclei are characterized by not only minimum values of the (7, n) reaction threshold, 1.665 and 2.225 MeV, respectively, but also by an abrupt growth of the reaction cross-section near the threshold. The latter dictates the specific shape of the photoneutron spectrum with a high density in the low-energy range. Nuclei with a single valence neutron in the p-shell, such as 9Be and i3C, are best suited to be a target to produce low-energy polarized neutrons. Their photodesintegration proceeds dominantly via an Eltransition with the emission of neutrons from the pJ bound state to the s-wave continuum, while the residual nucleus remains in its ground state O+. The total angular momentum of the valence neutron is J = 3/2 for 9Be and J = l/2 for i3C, coinciding with the spin
225
of a target nucleus. The ( y,n) threshold was specified above for 9Be and it is equal to 4.946 MeV for 13C. The wave function of a valence neutron in a p-shell bound state with total angular momentum J and a zero spin residual nucleus can be written in the form
is the spinor, describing the neutron state Here + with the projection u of the l/2 spin on an axis z, directed along the MB beam; Y,,(L), 4) is the sperical harmonic and C$@ are the Clebsh-Gordan coefficients, The amplitudes &+,(I), where M is a projection of spin J on an axis z, specify the initial spin state of the target nucleus. The probabilities ]a~( J) I2 do not depend on M when the target nuclei are nonpolarized. An absorption of a right/left polarized MB quantum in the case of a El-process leads to an increase/decrease in the orbital momentum projection m by unity, while the spin projection IT remains unchanged. As the projection m in the s-wave final state is zero, the amplitude u,” ( l/2) of the s-wave neutron final state with the projection u of the l/2 spin on the MB beam axis is determined by the product &l/2)
N uM(J)C;&
(3)
for right/left polarized MB radiation. We see that only the target nuclei with projection M = (+ F 1 participate in the El photodesintegration process induced by right/left polarized MB radiation leading to the production of the s-wave neutrons with projection cr. Note, that the angular distribution of the s-wave photoneutrons is isotropic, so the amplituoes a,( l/2) do not depend on the direction of the neutron emission. For a non-polarized target the neutron polarization equals (a) = *11-43(5+ Pn = 1/2 8
1) ’
(4)
where (a) =Ccrla,f(l/2)12 ,&l/:),2
N (c$/J’.U
I
Cl&l/2)12,
(5)
It follows that in the case of the right polarized MB radiation p,, = -0.5 for 9Be and pn = 1 for 13C. Pho-
I.P. Eremeev, A.L. Barabunov/ Physic& Letters B 401 (1997) 224-228
226
toneutrons emitted are polarized along the MB beam axis independently of the direction of their emission. In the general case of a direct El-transition from a p-shell state to the final state with orbital momentum I and total angular momentum j of the neutron with respect to the zero spin residual nucleus we get for the polarization averaged over all angles of emission Pn =
(3/4+j(j+I)-1(1+1))(2+j(j+l)-J(J+l)) Y(j+
1) (6)
In reality, 1 equals to 0 or 2 for a El-transition from a p-shell state, while the parity of the final state should be opposite to that of the initial state. If 1 = 0 and j = l/2 we return to the above result for s-wave final neutrons. The spectral density of photoneutrons produced in a target by the MB radiation formed by the single passage of an electron through a spatially periodic magnetic field is determined by the expressions
At E = 50 GeV mentioned above and ha = 5-6 cm, that is, at as small period as technically possible, the energy range of practical interest, namely E > 1.5 MeV, could be attained only when the higher harmonics of the radiation spectrum with k > 35 are used. It is fairly difficult to calculate the spectral angular characteristics of the undulator elliptically polarized radiation for the required great number of harmonics (about 200). Thus, we have restricted our consideration by an asymptotic case of a wiggler to estimate the spectral and integral intensity of polarized y-quanta according to the results of Ref. [ 51. The spectral density of the elliptically polarized yquanta emitted by an electron in a direction 0, = 0 in a wiggler with a number of periods NO was determined from the expression 8e2 NO E, N,I(E,)
x = f+,
Nrll(&)
x *
[1 - exp ( -Z,L)] Y
E
n
(Ey)
=A-* ACE,
,
Y
- E,n),
(8)
where NY1 is the spectral density of MB y-quanta per electron; A is the mass of the target nucleus; Er, E,, and Ey,, are the energies of the y-quantum, photoneutron and the (y, n) reaction threshold, respectively; a,( E,) and rry,,( E,) are the total cross-section and the cross-section of the (y, n) reaction for y-quanta of energy E,, respectively; X, is the macroscopic crosssection of attenuation for y-quanta in a target of length L along the MB beam. The energy of y-quanta emitted by an electron in the field ( 1) is determined by the expression
(9) where Afl = Aa/2y2, y = E/mc2, KxcY) = eH,o(,qAo/ 2n-mc2, k is the radiation harmonic number, 0, is the angle between the y-quantum emission direction and the z axis. Emitted at the angle 0, = 0 are only the odd harmonics and only the first one when H.,Q= HYo.
-
hcG--
c
Fx(Kx, z)
C
JG
+ F;(K,,
;)
c1,
(10)
where E,Q = he/h@, EC = (3/4r)eA,,HYoy2 is the “critical” energy of the MB spectrum, Ace is the Compton wavelength of an electron, the functions F, and FY are defined in Ref. [ 51. The degree of the circular polarization of emitted y-quanta was determined as Qy(fGt
Ey)
= 2JFx(Kx,EyIEC)FY(Kx,Ey/~,) fi(Kx,E,IE,)
+ &(K,,
E,/E,)
(11) ’
The photoneutron spectrum has been calculated at E = 50 GeV for a ‘Be target and the circularly polarized MB radiation from a wiggler with a length Lo = Naha = 900 cm, a period Aa = 12 cm, H>o = 2.3 T and K, = 1. The chosen values for E and H,o correspond to EC = 4.0 MeV. The value of K, = 1 has been chosen because a compromise has to be reached between the MB intensity and the degree of its polarization. The photoneutron spectrum provided by the linearly polarized MB radiation (K, = 0) has been calculated for comparison. The spectra normalized to a single passage of one electron through a wiggler are shown in Fig. 1. Nonpolarized neutrons are produced by linearly polarized y-quanta. The data [ 61 of the precision measurements
I.P. Eremeev. A.L. Barabanov /Physics Letters B 401 (1997) 224-228
227
Table 1 The characteristics of photoneutrons
N,, x IO6 , n/keVlel
.-.
MB polarization
Linear
Circular
QY
0 36 0 0.20
0.9 17 0.45-0.65 0.05
&I, de1 Ptl N,,!, n/e1
,
10
. * ..*..
1
*
100
I
1000
.
.
..I
\J
10000
E, , keV Fig. 1. The spectra of polarized (solid curve) and non-polarized (dashed curve) photoneutrons produced in the 9Be target by circularly and linearly polarized MB y-rays, respectively.
of the (y, n) cross-sections for Be were used for the calculation. The spectrum exhibits a high density of neutrons in the resonance energy range. The extrapolation of the results of Ref. [6] to zero shows that a spectral density of neutrons in the region below E, - E,, = 0.5 keV should be rather high due to the recoil of nuclei emitting photoneutrons. The kinematic corrections to the neutron energy E,, for emission angles of more than 90” for Be amount to 200400 eV to be sufficient to shift the zero of the E,, scale to the region of the noticeable values of gy,n in the E, - E,, scale.
According to Ref. [ 71 the total cross section of the 9Be( n, y)8Be reaction is determined mainly by a direct El-transition of neutron from ps/2-shell to continuum si/2- and d3/2-, dsl2-states for the energies Ey < 10 MeV. So only the l/2+, 3/2+ and 5/2+ excited states of the 9Be nucleus are significant. The contributions of the l/2- and 5/2- low-lying excited states of the 9Be, populated by E2 and Ml transitions, to the photoneutron spectra are small and may be neglected. The low-energy region of the spectra in Fig. 1 results from the emission of the s1/z-wave neutron (1 = 0, j= l/2), whiIe the next part of those is due to the dslz-wave (1 = 2, j = 512). So we can use the above described formalism to estimate the neutron polarization for these two parts of the spectrum. The magnitudes of the neutron polarization calculated by Eq. (6) for fully circularly polarized MB y-quanta are equal to pn = -0.5 and p,, = 0.7, respectively. Taking into account that the polarization of emitted y-quanta for the chosen wiggler parameters equals QY N 0.9, we
get the values of the neutron polarization P, = pnQy, shown in Fig. I. The third bump of the photoneutron spectrum, presented in Fig. 1, results from two different processes (see Ref. [ 71) . On the one hand, d3p- and ds/n-wave neutrons are emitted, and the residual *Be nucleus remains in its ground state Of. On the other hand, for E, 2 4.6 MeV a new channel of the reaction arises, corresponding to the sr/2-wave neutron emission while the *Be remains in its first excited state 2+. Note that in the latter process the total angular momentum J of the n+8Be system equals 3/2 or 5/2. Thus an estimate of the neutron polarization is difficult as not only the different weights of the listed contributions but also their interference should be properly accounted for. The calculation of the neutron polarization may be performed in the framework of some model of the reaction. However, the result will be model dependent. Therefore it would be more reasonable to determine the neutron polarization in this part of spectrum experimentally. For this reason we do not consider here the neutron polarization in the third bump. The integral characteristics expected have been calculated for the above conditions by integration over the ‘y-rays and neutron spectra. The results obtained are listed in Table 1. The table symbols are as follows: Q, is the degree of MB circular polarization; N,i is the total number of y-quanta emitted in the energy range E, 2 1.5 MeV by an electron in its single passage through the wiggler; P, = pnQr is the degree of the neutron polarization; N,I is the yield of photoneutrons per electron passage through the wiggler. The region length of the neutron production in the Be target is taken to be equal L N l/X,( E,) . If the magnitudes of E and H,o are increased to 70 GeV and 4.5-5 T, respectively, to correspond to a value of EC 21 15-17 MeV, the integral yield N,,t could be raised to 0.3 n/e1 for polarized neutrons and 1.0 n/e1 for non-polarized ones. For this reason the values
228
I.P. Eremeev, A.L. Barabanov/ Physics Letters B 401 (1997) 224-228
given in Table 1 should be considered as a lower limit for the possible values of the produced photoneutrons. It is evident from the data presented that the proposed approach has considerable promise for the use in fundamental investigations. This results from their characteristics such as: - a large pulsed neutron intensity and flux in combination with an ultrashort duration; - a possibility to produce polarized neutrons and to vary simply the degree and direction of their polarization; - a specific shape of the spectrum with a great density in the energy range of resonance neutrons; - a possibility to change simply the spectral end point in the wide energy region; - a minimum radiation loading the target and na radionucfides as compared with the other known methods of the neutron production. The corresponding source of polarized neutrons could be best realized on modern storage rings with an electron energy E 2 30 GeV and average current > 10 mA, such as LEP or HERA, whose beam parameters (see [2] and [ 81, respectively) allow the time average and peak flux of the polarized neutrons on a 9Be target surface to amount to N 10’6-10’7 n/cm*.s and - 5 . 10i9-5. 10” n/cm*+, respectively, at a neutron pulse duration determined as rll = L/c N 5. lo-‘O s. We note for comparison that at the best of the modern pulsed neutron sources, such as LANSCE and ISIS spallation sources, the average and peak flux of non-polarized fast neutrons on a surface of 238U,W or Ta targets are equal to N 5. 10’3-2. 1014n/cm*+ and N 1018-5 . 1018 n/cm*.s, respectively [9,10]. To produce slow polarized neutrons one uses Hz0 moderator and proton polarizer resulting in a neutron loss. Indeed, a fraction of fast neutrons incident to the surface of rectangular Hz0 moderators placed near
the targets amounts to 0.05-0.1 of the total number of produced neutrons. Transmission through a proton polarizer usually used to provide a degree of the neutron polarization near to the presented above in Table 1 does not exceed 0.2. Therefore, only a part of - lo-* of the total flux of the fast neutrons from the target can be used to produce slow polarized neutrons at the above spallation sources. The detailed calculation of the averaged and pulsed parameters for the proposed source in the case of both polarized and non-polarized neutrons and their comparison with the parameters of modern neutron sources is of special interest and will be carried out in a following paper. We are grateful to D.I? Grechukhin and D.F. Zaretsky taking interest in the problem. We thank the referee drawing our attention to the Ref. [3], unfortunately, being unavailable for us. References
[ I 1 II? Eremeev, JETP Lett 27 ( 1978) 10. [2] A. Hofmann, Phys. Rep. 64 ( 1980) 253. [3] G.C. Baldwin, Report LA-9051 (1981). [4] 1.P Eremeev, in: Proc. of the 1995 Particle Accelerator Conference and International Conference on High Energy Accelerators (Dallas, May 1995), Vol. I, p. 146 (1996). [S] H. Kitamura, Synchrotron Radiation News 5 ( 1992) 14. [6] B.L. Berman, R.L. Van Hemert, CD. Bowman, Phys. Rev. 163 (1967) 958. 171 T. Aurdal, 2. Naturforschung 24a ( 1969) I 188. IS] R. Brinkmann, in: Proc. of the 1995 Particle Accelerator Conference and International Conference on High Energy Accelerators (Dallas, May 1995). Vol. 1, p. 406 (1996). [9] PW. Lisowski, C.D. Bowman, G.J. Russell. S.A. Wender, Nucl. Sci. Eng. 106 (1990) 208. [IO] C.C. Wilson, Neutron News 6 (1995) 27.