- Email: [email protected]
Investigation of solid D2 , O2 and CD4 for ultracold neutron production
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 611 (2009) 252–255
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Investigation of solid D2 , O2 and CD4 for ultracold neutron production F. Atchison a, B. Blau a, K. Bodek b, B. van den Brandt a, T. Bry´s a,1, M. Daum a, P. Fierlinger a,2, A. Frei c, P. Geltenbort d, P. Hautle a, R. Henneck a, S. Heule a,3, A. Holley e, M. Kasprzak a,4,5,, K. Kirch a,, b,6 ´ , C.-Y. Liu f, C.L. Morris g, A. Pichlmaier a, C. Plonka d, A. Knecht a,3, J.A. Konter a, M. Kuzniak h g f Y. Pokotilovski , A. Saunders , Y. Shin , D. Tortorella c, M. Wohlmuther a, A.R. Young e, J. Zejma b, G. Zsigmond a a
Paul Scherrer Institut (PSI), CH-5132 Villigen PSI, Switzerland Institute of Physics, Jagiellonian University, Cracow, Poland Technische Universit¨ at M¨ unchen, M¨ unchen, Germany d Institut Laue-Langevin (ILL), Grenoble, France e North Carolina State University, Raleigh, USA f Indiana University, Bloomington, USA g Los Alamos National Laboratory, Los Alamos, USA h Joint Institute for Nuclear Research, Dubna, Russia b c
a r t i c l e in f o
a b s t r a c t
Available online 5 August 2009
We have investigated the properties of the ultracold neutron converter materials deuterium D2 , oxygen O2 and heavy methane CD4 in the temperature range between 8 K and room temperature. The experimental program was performed at the FUNSPIN beamline of the Swiss Spallation Neutron Source (SINQ) at Paul Scherrer Institut (PSI). In this paper the measured cold neutron total cross-sections for D2, O2 and CD4 are presented. & 2009 Published by Elsevier B.V.
Keywords: Ultracold neutrons Cold neutron scattering Moderation UCN converters
1. Motivation The development of high intensity ultracold neutron (UCN) sources is important for improving the accuracy of the experiments investigating fundamental properties of the neutron, e.g. the search for the electric dipole moment [1]. Presently there are several projects to build new UCN sources in order to provide the desired increase in intensity. The essential issue is the efficient use of an UCN converter. At the UCN source at PSI, due to the use of solid deuterium as UCN converter, the UCN density will be increased by about two orders of magnitude compared to the strongest source currently available (about 10 UCN=cm3 at Institut Laue-Langevin (ILL)). Detailed knowledge about the properties of the converter material is important for optimal source performance. The main
Corresponding authors.
E-mail addresses: [email protected] (M. Kasprzak), [email protected] (K. Kirch). 1 ¨ Also at Institute for Technical Chemistry, ETH Zurich, CH, Switzerland. 2 ¨ Munchen, ¨ ¨ Present address: Technische Universitat Munchen, Germany. 3 ¨ Also at Physik-Institut, University of Zurich, CH, Switzerland. 4 ¨ subatomare Physik, Austrian Academy of Also at Stefan Meyer Insitut fur Sciences, Vienna, Austria. 5 University of Fribourg, CH, Switzerland. 6 Also at Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland. 0168-9002/$ - see front matter & 2009 Published by Elsevier B.V. doi:10.1016/j.nima.2009.07.072
efforts are directed towards investigations of superfluid helium and solid deuterium ðD2 Þ. We have extended the studies of UCN converters and investigated the new candidate converter materials solid heavy methane ðCD4 Þ and solid oxygen ðO2 Þ.
2. Experiment The experiments were performed at the FUNSPIN beamline at PSI. We have measured the production of UCN from a cold neutron (CN) beam in D2 [2], O2 and CD4 and the CN transmission through all three materials. In order to understand the underlying processes of the UCN production in gaseous and solid deuterium the CN energy dependent UCN production was measured [3]. In this paper we present the CN transmission results in a form of total cross-sections. The idea of the experiment is simple, CN arrive, via a ‘‘flight tube’’ (1 in Fig. 1), to the target cell (2); the CN and UCN leaving the cell are measured by the detection system. The target cell is mounted on a cryostat and can be filled with D2 , O2 or CD4 (see Table 1), as appropriate, in the temperature range between 8 K and room temperature. The CN interact with the material in the cell and some of them get downscattered to UCN energies. Both, the CN and UCN enter the guide system following the target cell and after roughly 0.6 m UCN are separated from CN by a mirror (3)
ARTICLE IN PRESS F. Atchison et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 252–255
253
Fig. 1. A 3D view of the experimental setup. 1—CN guide, 2—cryostat with the target cell, 3 and 4—UCN reflecting mirrors, 5—entrance UCN shutter, 6—storage tube, 7—exit UCN shutter, 8—UCN detector, 9—CN chopper, 10—CN TOF tube, 11—CN detector. For the CN transmission and UCN production measurements we have used the full CN beam. For the CN energy dependent UCN production measurements, a velocity selector was mounted upstream of the cryostat.
Table 1 Temperatures of phase transitions in D2 , O2 and CD4 .
Boiling point (K) Melting point (K) Solid Phases
D2
CD4
O2
23.5 18.7
112 89.9 27:1 KoIo89:9 K 22:1 KoIIo27:1 K IIIo22:1 K
90.2 54.8 43:8 Kogo54:4 K 23:9 Kobo43:8 K ao23:9 K
Fig. 2. Measured total neutron scattering cross-sections per molecule as a function of the in-medium neutron energy for gaseous (25 K), liquid (19 K) and solid (18 K) D2 . The previously published data (see Refs. [6,7]) are completed with the new data coming from the transmission TOF measurements with CN. Comparing the different slopes of cross-sections of gas, liquid and solid D2 one can notice a rapid increase in the cross-section for solid and liquid D2 above the Bragg cut-off energy due to the interference effects arising from the correlation in molecular positions, while for gas no interference effects are visible at this energy.
which is a silicon wafer coated with UCN reflecting material with high Fermi potential.7 UCN are reflected upwards by this mirror
7 In fact during the experiment two types of the UCN mirror have been used, Ni-coated Si wafer and diamond-like carbon (DLC) coated Al foil.
Fig. 3. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid D2 at 18 (circles) and 8 K (stars). The solid, dashed and dotted lines show the theoretical elastic crosssection (the sum of coherent and incoherent) calculated by taking into account solid D2 crystal lattice parameters. The solid line represents the total elastic crosssection for a polycrystalline structure while the dashed and dotted ones show the elastic cross-section for crystals grown in specific directions. The comparison between the experimental data and theoretical cross-sections should be treated qualitatively i.e. in terms of understanding the structure of the deuterium crystals grown in the experiment. The measured cross-sections lie between the calculated cross-sections for random polycrystal and for oriented polycrystalline structure suggesting that the measured sample was in some intermediate state between random and oriented polycrystal. Additional hints come from the comparison of the data at 18 and 8 K (see also Figs. 4 and 5), higher cross-sections at 8 K indicate more random polycrystalline structure which is in agreement with the optical observation of the crystal as well as with the Raman spectra (see Ref. [5]).
Fig. 4. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid D2 at 18 K (triangles), 17 K (stars), 14 K (diamonds) and 8 K (squares). In the Bragg region the crosssection grows with lowering the temperature of the sD2 crystal, while it decreases for longer wavelength.
and after 1 m are again reflected by a second mirror (4) into a horizontal guide section. This section consists of a storage tube (6) and two UCN shutters: the entrance shutter (5) and the exit shutter (7). The UCN that passed the storage tube are later detected by the 3He UCN detector (8). The assembly of items 5–8 is rotated by 901 around the vertical guide so that the UCN detector is moved out of the CN beam axis. The CN are transmitted
ARTICLE IN PRESS 254
F. Atchison et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 252–255
Fig. 5. Comparison of the measured total neutron scattering cross-sections between three different sD2 crystals at 8 K. Two crystals were frozen from the liquid phase at the same conditions (stars and squares) and one was grown from the gas phase (circles). The cross-sections in the Bragg region differ significantly while they are the same in the region above the Bragg cut-off wavelength. This indicates that CN scattering (Bragg region) is very sensitive to the specific crystal structure. Those data also show that it is difficult to grow identical crystals i.e. with the same Bragg scattering pattern, even under very similar conditions. The average total cross-section, however, is not particularly sensitive to the crystal structure.
Fig. 6. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid CD4 in phase I at two different temperatures at 64 K (circles) and 28 K (stars). The Bragg cut-off is at about the same wavelength, but the cross-section in the Bragg region is higher at lower temperature. In the region above the Bragg cut-off wavelength the crosssection is higher and slightly increasing with wavelength suggesting some thermal upscattering. This behavior of the cross-section is similar for solid D2 (see Fig. 4). The cross-section above the Bragg cut-off wavelength is about 9 b/molecule which is consistent with the incoherent cross-section of the D atoms, i.e. 4 2:05 barn).
through the lower mirror (3) and then pass through a chopper (9), enter the time of flight tube (10) and are detected in the CN detector (11). More details of the setup can be found in Refs. [4,5].
3. The results The neutron total cross-sections were determined from the neutron beam attenuation in the measured sample. The neutron
Fig. 7. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid CD4 in different phases (the data points overlap, phase I (circles), phase II (stars), phase III (squares)). The cross-sections are the same suggesting no change in the crystal structure, this is in agreement with the crystallographic data [8]. It is interesting to compare these results with Figs. 6 and 4. The fact that the cross-section does not change with lowering the temperature might indicate that the sCD4 sample obtained at 28 K was a random polycrystal. It is also worth to note that the phase change does not influence the crystal structure strongly, it can be seen, however, in the Raman spectra [5].
Fig. 8. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid (circles) and liquid (stars) CD4 . The behavior of the cross-sections is similar to D2 cross-sections (see Fig. 2). For liquid CD4 the cross-section is higher above and below the Bragg cutoff.
count-rate N0 has been measured for the beam passing through an empty target cell (pressure po5 104 mbar) and the neutron count-rate N1 for the beam passing through the target cell filled with D2 , O2 or CD4 as appropriate. These count-rates are related through: N1 ðlÞ ¼ N0 ðlÞexpðrstot ðlÞlÞ
ð1Þ
where l is the neutron wavelength, r is the density of the sample, l is the length of the cell and stot is the total cross-section. The total cross-sections stot values obtained are shown in Figs. 2–10. The results are interpreted in terms of neutron scattering theory. For all three substances we have observed coherent scattering arising from the crystal lattice structure.
ARTICLE IN PRESS F. Atchison et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 252–255
Fig. 9. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for three phases of solid oxygen. It is interesting to note that the cross-section changes with the phase change. In the cubic g-phase (triangles) one pronounced Bragg edge is visible (starting at ˚ while in the rhombohedral b-phase (stars) two Bragg edges show about 7 A) ˚ up—one at about 8 A˚ and the second at 6 A—and in the monoclinic a-phase (spheres) three Bragg edges appear—two basically the same as for the b-phase and ˚ Those observations could be explained by the one additional at about 10 A. different crystal structures and thus different lattice parameters of a-, b-, g-phases of solid oxygen. Above the Bragg cut-off wavelength the cross-section at low temperatures tends to 0 which is in agreement with the fact that oxygen (16O) has no incoherent cross-section.
4. Conclusions The interest in developing new high intensity UCN sources requires experimental data relevant to characterize the neutron thermalization process like total cross-sections. In this paper the results from the CN scattering experiment in the form of total cross-sections for D2, O2 and CD4 at various temperatures have been presented. That data can be of great use for improving the scattering kernels for cryogenic materials of interest as cold and ultracold neutron moderators.
Acknowledgments We are grateful to the accelerator crew and SINQ staff for providing excellent beam conditions and to the various technical
255
Fig. 10. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid (triangles) and liquid (stars) oxygen. Again the behavior of the liquid O2 cross-sections is similar to the D2 and CD4 cross-sections, the increase in the cross-section in the Bragg scattering region is visible.
support services, whose help have made these experiments possible. We wish to especially acknowledge the support of W. Arrigoni, M. Meier and P. Schurter. Help of K. Clausen, G. Frei, E. Lehmann, T. Scherer, M. Luethy and M. Wiedemeier is gratefully acknowledged. We thank E.Widmann, A. Wokaun and H. Zmeskal for discussions. We want to thank R. Granada for the theoretical support.
References [1] [2] [3] [4] [5]
C.A. Baker, et al., Phys. Rev. Lett. 97 (2006) 131801. F. Atchison, et al., Phys. Rev. C 71 (2005) 054601. F. Atchison, et al., Phys. Rev. Lett. 99 (2007) 262502. K. Bodek, et al., Nucl. Instr. and Meth. A 533 (2004) 491. M. Kasprzak, Ultracold neutron converters, Ph.D. Thesis, University of Vienna, 2008. [6] F. Atchison, et al., Phys. Rev. Lett. 94 (2005) 212502. [7] F. Atchison, et al., Phys. Rev. Lett. 95 (2005) 182502. [8] V.G. Manzhelii, et al., Begell House Inc. Publishers, 1999.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Investigation of solid D2 , O2 and CD4 for ultracold neutron production F. Atchison a, B. Blau a, K. Bodek b, B. van den Brandt a, T. Bry´s a,1, M. Daum a, P. Fierlinger a,2, A. Frei c, P. Geltenbort d, P. Hautle a, R. Henneck a, S. Heule a,3, A. Holley e, M. Kasprzak a,4,5,, K. Kirch a,, b,6 ´ , C.-Y. Liu f, C.L. Morris g, A. Pichlmaier a, C. Plonka d, A. Knecht a,3, J.A. Konter a, M. Kuzniak h g f Y. Pokotilovski , A. Saunders , Y. Shin , D. Tortorella c, M. Wohlmuther a, A.R. Young e, J. Zejma b, G. Zsigmond a a
Paul Scherrer Institut (PSI), CH-5132 Villigen PSI, Switzerland Institute of Physics, Jagiellonian University, Cracow, Poland Technische Universit¨ at M¨ unchen, M¨ unchen, Germany d Institut Laue-Langevin (ILL), Grenoble, France e North Carolina State University, Raleigh, USA f Indiana University, Bloomington, USA g Los Alamos National Laboratory, Los Alamos, USA h Joint Institute for Nuclear Research, Dubna, Russia b c
a r t i c l e in f o
a b s t r a c t
Available online 5 August 2009
We have investigated the properties of the ultracold neutron converter materials deuterium D2 , oxygen O2 and heavy methane CD4 in the temperature range between 8 K and room temperature. The experimental program was performed at the FUNSPIN beamline of the Swiss Spallation Neutron Source (SINQ) at Paul Scherrer Institut (PSI). In this paper the measured cold neutron total cross-sections for D2, O2 and CD4 are presented. & 2009 Published by Elsevier B.V.
Keywords: Ultracold neutrons Cold neutron scattering Moderation UCN converters
1. Motivation The development of high intensity ultracold neutron (UCN) sources is important for improving the accuracy of the experiments investigating fundamental properties of the neutron, e.g. the search for the electric dipole moment [1]. Presently there are several projects to build new UCN sources in order to provide the desired increase in intensity. The essential issue is the efficient use of an UCN converter. At the UCN source at PSI, due to the use of solid deuterium as UCN converter, the UCN density will be increased by about two orders of magnitude compared to the strongest source currently available (about 10 UCN=cm3 at Institut Laue-Langevin (ILL)). Detailed knowledge about the properties of the converter material is important for optimal source performance. The main
Corresponding authors.
E-mail addresses: [email protected] (M. Kasprzak), [email protected] (K. Kirch). 1 ¨ Also at Institute for Technical Chemistry, ETH Zurich, CH, Switzerland. 2 ¨ Munchen, ¨ ¨ Present address: Technische Universitat Munchen, Germany. 3 ¨ Also at Physik-Institut, University of Zurich, CH, Switzerland. 4 ¨ subatomare Physik, Austrian Academy of Also at Stefan Meyer Insitut fur Sciences, Vienna, Austria. 5 University of Fribourg, CH, Switzerland. 6 Also at Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland. 0168-9002/$ - see front matter & 2009 Published by Elsevier B.V. doi:10.1016/j.nima.2009.07.072
efforts are directed towards investigations of superfluid helium and solid deuterium ðD2 Þ. We have extended the studies of UCN converters and investigated the new candidate converter materials solid heavy methane ðCD4 Þ and solid oxygen ðO2 Þ.
2. Experiment The experiments were performed at the FUNSPIN beamline at PSI. We have measured the production of UCN from a cold neutron (CN) beam in D2 [2], O2 and CD4 and the CN transmission through all three materials. In order to understand the underlying processes of the UCN production in gaseous and solid deuterium the CN energy dependent UCN production was measured [3]. In this paper we present the CN transmission results in a form of total cross-sections. The idea of the experiment is simple, CN arrive, via a ‘‘flight tube’’ (1 in Fig. 1), to the target cell (2); the CN and UCN leaving the cell are measured by the detection system. The target cell is mounted on a cryostat and can be filled with D2 , O2 or CD4 (see Table 1), as appropriate, in the temperature range between 8 K and room temperature. The CN interact with the material in the cell and some of them get downscattered to UCN energies. Both, the CN and UCN enter the guide system following the target cell and after roughly 0.6 m UCN are separated from CN by a mirror (3)
ARTICLE IN PRESS F. Atchison et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 252–255
253
Fig. 1. A 3D view of the experimental setup. 1—CN guide, 2—cryostat with the target cell, 3 and 4—UCN reflecting mirrors, 5—entrance UCN shutter, 6—storage tube, 7—exit UCN shutter, 8—UCN detector, 9—CN chopper, 10—CN TOF tube, 11—CN detector. For the CN transmission and UCN production measurements we have used the full CN beam. For the CN energy dependent UCN production measurements, a velocity selector was mounted upstream of the cryostat.
Table 1 Temperatures of phase transitions in D2 , O2 and CD4 .
Boiling point (K) Melting point (K) Solid Phases
D2
CD4
O2
23.5 18.7
112 89.9 27:1 KoIo89:9 K 22:1 KoIIo27:1 K IIIo22:1 K
90.2 54.8 43:8 Kogo54:4 K 23:9 Kobo43:8 K ao23:9 K
Fig. 2. Measured total neutron scattering cross-sections per molecule as a function of the in-medium neutron energy for gaseous (25 K), liquid (19 K) and solid (18 K) D2 . The previously published data (see Refs. [6,7]) are completed with the new data coming from the transmission TOF measurements with CN. Comparing the different slopes of cross-sections of gas, liquid and solid D2 one can notice a rapid increase in the cross-section for solid and liquid D2 above the Bragg cut-off energy due to the interference effects arising from the correlation in molecular positions, while for gas no interference effects are visible at this energy.
which is a silicon wafer coated with UCN reflecting material with high Fermi potential.7 UCN are reflected upwards by this mirror
7 In fact during the experiment two types of the UCN mirror have been used, Ni-coated Si wafer and diamond-like carbon (DLC) coated Al foil.
Fig. 3. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid D2 at 18 (circles) and 8 K (stars). The solid, dashed and dotted lines show the theoretical elastic crosssection (the sum of coherent and incoherent) calculated by taking into account solid D2 crystal lattice parameters. The solid line represents the total elastic crosssection for a polycrystalline structure while the dashed and dotted ones show the elastic cross-section for crystals grown in specific directions. The comparison between the experimental data and theoretical cross-sections should be treated qualitatively i.e. in terms of understanding the structure of the deuterium crystals grown in the experiment. The measured cross-sections lie between the calculated cross-sections for random polycrystal and for oriented polycrystalline structure suggesting that the measured sample was in some intermediate state between random and oriented polycrystal. Additional hints come from the comparison of the data at 18 and 8 K (see also Figs. 4 and 5), higher cross-sections at 8 K indicate more random polycrystalline structure which is in agreement with the optical observation of the crystal as well as with the Raman spectra (see Ref. [5]).
Fig. 4. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid D2 at 18 K (triangles), 17 K (stars), 14 K (diamonds) and 8 K (squares). In the Bragg region the crosssection grows with lowering the temperature of the sD2 crystal, while it decreases for longer wavelength.
and after 1 m are again reflected by a second mirror (4) into a horizontal guide section. This section consists of a storage tube (6) and two UCN shutters: the entrance shutter (5) and the exit shutter (7). The UCN that passed the storage tube are later detected by the 3He UCN detector (8). The assembly of items 5–8 is rotated by 901 around the vertical guide so that the UCN detector is moved out of the CN beam axis. The CN are transmitted
ARTICLE IN PRESS 254
F. Atchison et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 252–255
Fig. 5. Comparison of the measured total neutron scattering cross-sections between three different sD2 crystals at 8 K. Two crystals were frozen from the liquid phase at the same conditions (stars and squares) and one was grown from the gas phase (circles). The cross-sections in the Bragg region differ significantly while they are the same in the region above the Bragg cut-off wavelength. This indicates that CN scattering (Bragg region) is very sensitive to the specific crystal structure. Those data also show that it is difficult to grow identical crystals i.e. with the same Bragg scattering pattern, even under very similar conditions. The average total cross-section, however, is not particularly sensitive to the crystal structure.
Fig. 6. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid CD4 in phase I at two different temperatures at 64 K (circles) and 28 K (stars). The Bragg cut-off is at about the same wavelength, but the cross-section in the Bragg region is higher at lower temperature. In the region above the Bragg cut-off wavelength the crosssection is higher and slightly increasing with wavelength suggesting some thermal upscattering. This behavior of the cross-section is similar for solid D2 (see Fig. 4). The cross-section above the Bragg cut-off wavelength is about 9 b/molecule which is consistent with the incoherent cross-section of the D atoms, i.e. 4 2:05 barn).
through the lower mirror (3) and then pass through a chopper (9), enter the time of flight tube (10) and are detected in the CN detector (11). More details of the setup can be found in Refs. [4,5].
3. The results The neutron total cross-sections were determined from the neutron beam attenuation in the measured sample. The neutron
Fig. 7. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid CD4 in different phases (the data points overlap, phase I (circles), phase II (stars), phase III (squares)). The cross-sections are the same suggesting no change in the crystal structure, this is in agreement with the crystallographic data [8]. It is interesting to compare these results with Figs. 6 and 4. The fact that the cross-section does not change with lowering the temperature might indicate that the sCD4 sample obtained at 28 K was a random polycrystal. It is also worth to note that the phase change does not influence the crystal structure strongly, it can be seen, however, in the Raman spectra [5].
Fig. 8. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid (circles) and liquid (stars) CD4 . The behavior of the cross-sections is similar to D2 cross-sections (see Fig. 2). For liquid CD4 the cross-section is higher above and below the Bragg cutoff.
count-rate N0 has been measured for the beam passing through an empty target cell (pressure po5 104 mbar) and the neutron count-rate N1 for the beam passing through the target cell filled with D2 , O2 or CD4 as appropriate. These count-rates are related through: N1 ðlÞ ¼ N0 ðlÞexpðrstot ðlÞlÞ
ð1Þ
where l is the neutron wavelength, r is the density of the sample, l is the length of the cell and stot is the total cross-section. The total cross-sections stot values obtained are shown in Figs. 2–10. The results are interpreted in terms of neutron scattering theory. For all three substances we have observed coherent scattering arising from the crystal lattice structure.
ARTICLE IN PRESS F. Atchison et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 252–255
Fig. 9. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for three phases of solid oxygen. It is interesting to note that the cross-section changes with the phase change. In the cubic g-phase (triangles) one pronounced Bragg edge is visible (starting at ˚ while in the rhombohedral b-phase (stars) two Bragg edges show about 7 A) ˚ up—one at about 8 A˚ and the second at 6 A—and in the monoclinic a-phase (spheres) three Bragg edges appear—two basically the same as for the b-phase and ˚ Those observations could be explained by the one additional at about 10 A. different crystal structures and thus different lattice parameters of a-, b-, g-phases of solid oxygen. Above the Bragg cut-off wavelength the cross-section at low temperatures tends to 0 which is in agreement with the fact that oxygen (16O) has no incoherent cross-section.
4. Conclusions The interest in developing new high intensity UCN sources requires experimental data relevant to characterize the neutron thermalization process like total cross-sections. In this paper the results from the CN scattering experiment in the form of total cross-sections for D2, O2 and CD4 at various temperatures have been presented. That data can be of great use for improving the scattering kernels for cryogenic materials of interest as cold and ultracold neutron moderators.
Acknowledgments We are grateful to the accelerator crew and SINQ staff for providing excellent beam conditions and to the various technical
255
Fig. 10. Measured total neutron scattering cross-sections in the region of Bragg scattering as a function of the neutron wavelength for solid (triangles) and liquid (stars) oxygen. Again the behavior of the liquid O2 cross-sections is similar to the D2 and CD4 cross-sections, the increase in the cross-section in the Bragg scattering region is visible.
support services, whose help have made these experiments possible. We wish to especially acknowledge the support of W. Arrigoni, M. Meier and P. Schurter. Help of K. Clausen, G. Frei, E. Lehmann, T. Scherer, M. Luethy and M. Wiedemeier is gratefully acknowledged. We thank E.Widmann, A. Wokaun and H. Zmeskal for discussions. We want to thank R. Granada for the theoretical support.
References [1] [2] [3] [4] [5]
C.A. Baker, et al., Phys. Rev. Lett. 97 (2006) 131801. F. Atchison, et al., Phys. Rev. C 71 (2005) 054601. F. Atchison, et al., Phys. Rev. Lett. 99 (2007) 262502. K. Bodek, et al., Nucl. Instr. and Meth. A 533 (2004) 491. M. Kasprzak, Ultracold neutron converters, Ph.D. Thesis, University of Vienna, 2008. [6] F. Atchison, et al., Phys. Rev. Lett. 94 (2005) 212502. [7] F. Atchison, et al., Phys. Rev. Lett. 95 (2005) 182502. [8] V.G. Manzhelii, et al., Begell House Inc. Publishers, 1999.