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Proposal for an improved method to determine the spin of low energy neutron resonances
Abrahams, K.
Physica 29
331-334
1963
PROPOSAL FOR AN IMPROVED METHOD TO DETERMINE THE SPIN OF LOW ENERGY NEUTRON RESONANCES*) by K ABRAHAMS Institutt for Atomenergi, Kjeller, Norge
Synopsis For a nuclide having a low energy neutron resonance, built in a ferro- or ferrimagnetic single crystal, the energy dependence of the cross section for nuclear scattering of neutrons can be found by determining the energy dependence of the ratio of the nuclear and magnetic scattering cross sections. This is possible because of the fact that the magnetic scattering cross section is independent of the energy of the neutrons if a Bragg reflection from a fixed crystal plane is used. The energy dependence of the nuclear cross section can be used to determine the spin of the resonance.
Introduction. Of the about 150 neutron resonances below 10 eV, only a few have a known spin value J. It is known that for these low energy resonances ] = I ± t if I is the spin of the capturing nucleus; there are only a few exceptions from this rule 1). As soon as the spin of the resonant state is known, its neutron width can be found more accurately. This entity, together with the statistical distribution of the spins of the excited states, enters several theoretical contemplations 2). Several methods are used for the determination of the spins of some of these resonances 2) 3). We can divide the existing methods into four classes: 1) The methods using capture of the neutrons, which may be polarized or not, in unoriented or oriented nuclei, studying anisotropy, polarization, or angular correlation of the emitted radiation 3). 2) The use of oriented nuclei and polarized neutrons 4). Polarized neutrons are absorbed, in the case of ] = 1+ t, if the spin of the neutron has the same direction as the spin of the nucleus, in the case of] = I - t, if the spins of the neutron and the nucleus are anti-parallel. 3) The knowledge of the elastic scattering cross section as a function of energy can give information concerning the spin of the compound state because of interference between potential and resonance scattering 2) 5). 4) The measurement of elastic neutron scattering cross section for un*) Work sponsored jointly by Institutt for Atomenergi and Reactor Centrum Nederland.
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331 -
332
K. ABRAHAMS
polarized neutrons in magnetic substances with polarized nuclei, giving information concerning the spin because of interference between magnetic and resonance scattering. Such a method has been suggested by de Gennes 6), but so far no experiments utilizing this method have been reported. An improvement of the third method will be proposed, namely the measurement of the ratio of the magnetic and the nuclear scattering of neutrons elastically scattered from ferro- or ferrimagnetic single crystals; it is not necessary that the target nuclei are oriented. Description o] the method. The coherent scattering of neutrons can be divided into nuclear scattering and magnetic scattering. The nuclear scattering can be divided into potential or hard sphere scattering with scattering amplitude equal to the effective radius of the nucleus being spin independent, and resonance scattering due to intermediate formation of a compound nucleus with scattering amplitude, given by the BreitWignerfonnula, being dependent upon the spin of this compound nucleus 1). The magnetic scattering considered is that due to the interaction of the neutron magnetic moment with the magnetic moment of unpaired electron spins 7). In method three the spin of a resonance is determined by measuring the absolute elastic scattering cross section as a function of the energy. For the two different possible spins of the compound state] = I ± t one gets different energy dependence of the cross section. The difticulties attached to this method are due to the tact that one has to measure absolute scattering cross sections. This gives problems due to: background, self absorption in the target, multiple scattering, energy dependence of the detector efficiency, coherence effects, inelastic scattering, and broadening of the resonance peak due to Doppler effect 1) 8). All these disturbances are energy dependent and make the interpretation of the results difficult. This, together with the fact that for low energy resonances the scattering cross sections are small compared with the capture cross sections, is the reason that method three is rather seldom applied in the region of low energy resonances. To get rid of these difficulties the following method is proposed: A magnetized ferro- or ferrimagnetic single crystal containing the nuclide one is interested in, is used as a target. This single crystal is placed in a white neutron beam in such a. way that a Bragg reflected monochromatic neutron beam is obtained, having the desired wavelength given by Bragg's law nA = 2d sin e. Now the ratio of the intensities of nuclear and magnetic scattering is determined as a function of the energy with one of the methods mentioned below.
METHOD TO DETERMINE THE SPIN OF LOW ENERGY NEUTRON RESONANCES
333
1) The determination of the ratio of the intensities with a magnetic field in the direction of the scattering vector and 'with a magnetic field perpendicular to the scattering vector. With the magnetic field in the direction of the scattering vector only the nuclear scattering intensity is measured, with the magnetic field perpendicular to the scattering vector, the sum of the nuclear and the magnetic scattering is measured 7) *). 2) The determination of the ratio of the intensities with a magnetic field perpendicular to the scattering vector for temperatures below and above the Curie temperature of the target material. Due to the fact that the ordering of the magnetic moments of the target atoms disappears above the Curie temperature, in the first case the sum of nuclear and magnetic scattering, and in the second case just the nuclear scattering is measured 9) 11) "'). By determining the ratio of nuclear scattering and magnetic scattering as a function of energy for a given scattering plane, the energy dependence of the nuclear scattering can be found. This is especially easy because the magnetic scattering cross section is a constant if one varies the energy of the Bragg reflected beam such that one always reflects from the same scattering plane. This is because of the fact that the magnetic scattering cross section just depends on the energy through a form factor which is a function of sin 0/). and this is a constant namely n/2cl for a Bragg reflection 7). We then look apart from the Debye-Waller factor, which also enters the expression of the nuclear scattering, and thus drops out when taking the ratio of nuclear to magnetic scattering.
Discussion. The most evident field of application of the proposed method seems to be the spin determination of the low energy neutron resonances of the rare earth metals. These metals, however, do not follow the classical law of the angular dependence of the magnetic cross section 10). Also compounds of these elements with other magnetic elements could be studied 11). For all cases where method two or method four can be applied, the proposed method can be applied also, and seems easier because it is not so difficult to orient atomic moments as to orient nuclei. The first method has the advantage that it can be used for all nuclides, but special techniques for detection of the emitted radiation and eventually for the measurement of its polarization are necessary. Another possibility to measure the ratio of the nuclear and the magnetic ~) The measurement with a magnetic field perpendicular to the scattering vector may eventually be substituted by a measurement with an unmagnetizecl crystal, since this gives the sum of the nuclear cross section plus two thirds of the magnetic one.
334 METHOD TO DETERMINE THE SPIN OF LOW ENERGY NEUTRON RESONANCES
scattering amplitudes, is the determination of the polarization of the Bragg reflected neutron beam. This polarization will be caused by interference between nuclear and magnetic scattering. Only if the intensity of the magnetic scattering is weak and if the energy of the resonance is low, this method would compete with the proposed one. Acknowledgement. The author wants to thank Dr. T. Riste for illuminating discussions on magnetic scattering. Received 24-9- 2
REFERENCES I) Bollinger, L. M., in Nuclear Spectroscopy, edited by Fay Ajzenberg-Selove (Academic Press 1960) 417-450. 2) Sailor, V. L., Phys. Rev. IO-i (1956) 736. 3) Abrahams, K .. Lecture notes of the Advanced Course all Neutron Crystal Spectroscopy. Kjeller, Norway 1962. 4) Postma, H., e.a., Phys. Rev. 120 (1962) 979. 5) Saenz, A. W. and Pogdor, S., N.R.L. 5592,1961. 6) De Genncs, P. G., C. R. Acad. se, 2Ci2 (1961) 3571. 7) Bacon, G. E., Neutron Diffraction. (Clarendon Press 1955). 8) Brockhouse, B. N., Can. J. Phys, 31 (1953) 432. 9) Wilkinson, M. K, e.a.,]. appl, Phys, Supp1. 32, no. 3 (1961) 485. 10) Odiot, S. and Saint-James, D.,]. Phys, Chern. Solids 17 (1960),117. 11) Bcr t a u t, F., B.a., C. R. Acnd, Sc. 24:1 (1956) 898.
Physica 29
331-334
1963
PROPOSAL FOR AN IMPROVED METHOD TO DETERMINE THE SPIN OF LOW ENERGY NEUTRON RESONANCES*) by K ABRAHAMS Institutt for Atomenergi, Kjeller, Norge
Synopsis For a nuclide having a low energy neutron resonance, built in a ferro- or ferrimagnetic single crystal, the energy dependence of the cross section for nuclear scattering of neutrons can be found by determining the energy dependence of the ratio of the nuclear and magnetic scattering cross sections. This is possible because of the fact that the magnetic scattering cross section is independent of the energy of the neutrons if a Bragg reflection from a fixed crystal plane is used. The energy dependence of the nuclear cross section can be used to determine the spin of the resonance.
Introduction. Of the about 150 neutron resonances below 10 eV, only a few have a known spin value J. It is known that for these low energy resonances ] = I ± t if I is the spin of the capturing nucleus; there are only a few exceptions from this rule 1). As soon as the spin of the resonant state is known, its neutron width can be found more accurately. This entity, together with the statistical distribution of the spins of the excited states, enters several theoretical contemplations 2). Several methods are used for the determination of the spins of some of these resonances 2) 3). We can divide the existing methods into four classes: 1) The methods using capture of the neutrons, which may be polarized or not, in unoriented or oriented nuclei, studying anisotropy, polarization, or angular correlation of the emitted radiation 3). 2) The use of oriented nuclei and polarized neutrons 4). Polarized neutrons are absorbed, in the case of ] = 1+ t, if the spin of the neutron has the same direction as the spin of the nucleus, in the case of] = I - t, if the spins of the neutron and the nucleus are anti-parallel. 3) The knowledge of the elastic scattering cross section as a function of energy can give information concerning the spin of the compound state because of interference between potential and resonance scattering 2) 5). 4) The measurement of elastic neutron scattering cross section for un*) Work sponsored jointly by Institutt for Atomenergi and Reactor Centrum Nederland.
-
331 -
332
K. ABRAHAMS
polarized neutrons in magnetic substances with polarized nuclei, giving information concerning the spin because of interference between magnetic and resonance scattering. Such a method has been suggested by de Gennes 6), but so far no experiments utilizing this method have been reported. An improvement of the third method will be proposed, namely the measurement of the ratio of the magnetic and the nuclear scattering of neutrons elastically scattered from ferro- or ferrimagnetic single crystals; it is not necessary that the target nuclei are oriented. Description o] the method. The coherent scattering of neutrons can be divided into nuclear scattering and magnetic scattering. The nuclear scattering can be divided into potential or hard sphere scattering with scattering amplitude equal to the effective radius of the nucleus being spin independent, and resonance scattering due to intermediate formation of a compound nucleus with scattering amplitude, given by the BreitWignerfonnula, being dependent upon the spin of this compound nucleus 1). The magnetic scattering considered is that due to the interaction of the neutron magnetic moment with the magnetic moment of unpaired electron spins 7). In method three the spin of a resonance is determined by measuring the absolute elastic scattering cross section as a function of the energy. For the two different possible spins of the compound state] = I ± t one gets different energy dependence of the cross section. The difticulties attached to this method are due to the tact that one has to measure absolute scattering cross sections. This gives problems due to: background, self absorption in the target, multiple scattering, energy dependence of the detector efficiency, coherence effects, inelastic scattering, and broadening of the resonance peak due to Doppler effect 1) 8). All these disturbances are energy dependent and make the interpretation of the results difficult. This, together with the fact that for low energy resonances the scattering cross sections are small compared with the capture cross sections, is the reason that method three is rather seldom applied in the region of low energy resonances. To get rid of these difficulties the following method is proposed: A magnetized ferro- or ferrimagnetic single crystal containing the nuclide one is interested in, is used as a target. This single crystal is placed in a white neutron beam in such a. way that a Bragg reflected monochromatic neutron beam is obtained, having the desired wavelength given by Bragg's law nA = 2d sin e. Now the ratio of the intensities of nuclear and magnetic scattering is determined as a function of the energy with one of the methods mentioned below.
METHOD TO DETERMINE THE SPIN OF LOW ENERGY NEUTRON RESONANCES
333
1) The determination of the ratio of the intensities with a magnetic field in the direction of the scattering vector and 'with a magnetic field perpendicular to the scattering vector. With the magnetic field in the direction of the scattering vector only the nuclear scattering intensity is measured, with the magnetic field perpendicular to the scattering vector, the sum of the nuclear and the magnetic scattering is measured 7) *). 2) The determination of the ratio of the intensities with a magnetic field perpendicular to the scattering vector for temperatures below and above the Curie temperature of the target material. Due to the fact that the ordering of the magnetic moments of the target atoms disappears above the Curie temperature, in the first case the sum of nuclear and magnetic scattering, and in the second case just the nuclear scattering is measured 9) 11) "'). By determining the ratio of nuclear scattering and magnetic scattering as a function of energy for a given scattering plane, the energy dependence of the nuclear scattering can be found. This is especially easy because the magnetic scattering cross section is a constant if one varies the energy of the Bragg reflected beam such that one always reflects from the same scattering plane. This is because of the fact that the magnetic scattering cross section just depends on the energy through a form factor which is a function of sin 0/). and this is a constant namely n/2cl for a Bragg reflection 7). We then look apart from the Debye-Waller factor, which also enters the expression of the nuclear scattering, and thus drops out when taking the ratio of nuclear to magnetic scattering.
Discussion. The most evident field of application of the proposed method seems to be the spin determination of the low energy neutron resonances of the rare earth metals. These metals, however, do not follow the classical law of the angular dependence of the magnetic cross section 10). Also compounds of these elements with other magnetic elements could be studied 11). For all cases where method two or method four can be applied, the proposed method can be applied also, and seems easier because it is not so difficult to orient atomic moments as to orient nuclei. The first method has the advantage that it can be used for all nuclides, but special techniques for detection of the emitted radiation and eventually for the measurement of its polarization are necessary. Another possibility to measure the ratio of the nuclear and the magnetic ~) The measurement with a magnetic field perpendicular to the scattering vector may eventually be substituted by a measurement with an unmagnetizecl crystal, since this gives the sum of the nuclear cross section plus two thirds of the magnetic one.
334 METHOD TO DETERMINE THE SPIN OF LOW ENERGY NEUTRON RESONANCES
scattering amplitudes, is the determination of the polarization of the Bragg reflected neutron beam. This polarization will be caused by interference between nuclear and magnetic scattering. Only if the intensity of the magnetic scattering is weak and if the energy of the resonance is low, this method would compete with the proposed one. Acknowledgement. The author wants to thank Dr. T. Riste for illuminating discussions on magnetic scattering. Received 24-9- 2
REFERENCES I) Bollinger, L. M., in Nuclear Spectroscopy, edited by Fay Ajzenberg-Selove (Academic Press 1960) 417-450. 2) Sailor, V. L., Phys. Rev. IO-i (1956) 736. 3) Abrahams, K .. Lecture notes of the Advanced Course all Neutron Crystal Spectroscopy. Kjeller, Norway 1962. 4) Postma, H., e.a., Phys. Rev. 120 (1962) 979. 5) Saenz, A. W. and Pogdor, S., N.R.L. 5592,1961. 6) De Genncs, P. G., C. R. Acad. se, 2Ci2 (1961) 3571. 7) Bacon, G. E., Neutron Diffraction. (Clarendon Press 1955). 8) Brockhouse, B. N., Can. J. Phys, 31 (1953) 432. 9) Wilkinson, M. K, e.a.,]. appl, Phys, Supp1. 32, no. 3 (1961) 485. 10) Odiot, S. and Saint-James, D.,]. Phys, Chern. Solids 17 (1960),117. 11) Bcr t a u t, F., B.a., C. R. Acnd, Sc. 24:1 (1956) 898.