Quasistationary states of ultracold neutrons have been observed in a double-hump potential barrier. This potential barrier was created by sandwiching a thin film of aluminum between two thin copper films. Measurements of reflection from and transmission through such composite films displayed clear resonances. The resonance positions and widths are in agreement with calculations

Malik, S. S.

Scheckenhofer, H.

Steinhauser, K.-A.

Steyerl, A.

English

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University of Rhode IslandDigitalCommons@URIPhysics Faculty Publications Physics1980Observation of Quasibound States of the Neutronin MatterK.-A. SteinhauserA. SteyerlUniversity of Rhode Island, asteyerl@uri.eduSee next page for additional authorsFollow this and additional works at: https://digitalcommons.uri.edu/phys_facpubsTerms of UseAll rights reserved under copyright.This Article is brought to you for free and open access by the Physics at DigitalCommons@URI. It has been accepted for inclusion in Physics FacultyPublications by an authorized administrator of DigitalCommons@URI. For more information, please contact digitalcommons@etal.uri.edu.Citation/Publisher AttributionSteinhauser, K.-A., Steyerl, A., Scheckenhofer, H., & Malik, S. S. (1980). Observation of Quasibound States of the Neutron in Matter.Physical Review Letters, 44(20), 1306-1309. doi: 10.1103/PhysRevLett.44.1306Available at: http://dx.doi.org/10.1103/PhysRevLett.44.1306AuthorsK.-A. Steinhauser, A. Steyerl, H. Scheckenhofer, and S. S. MalikThis article is available at DigitalCommons@URI: https://digitalcommons.uri.edu/phys_facpubs/258VOLUME 44, NUMBER 20 PHYSICAL REVIEW LETTERS 19 MAY 19SOObservation of Quasibound States of the Neutron in MatterK.-A. Steinhauser, A. Steyerl, and H. ScheckenhoferFakultat fur Physik, Technische Universitat Miinchen, D-8046 Garching, GermanyS. S. MalikFakultat fur Physik, Technische Universitat Munchen, D-8046 Garching, Germany, and Physics DePartment,University of Rhode Island, Kingston, Rhode Island 08881(Received 29 February 1980)Quasistationary states of ultracold neutrons have been observed in. a double-hump po-tential barrier. This potential barrier was created by sandwiching a thin film of aluminumbetween two thin copper films. Measurements of reflection from and transmission throughsuch composite films displayed clear resonances. The resonance positions and widths arein agreement with calculations.PACS numbers: 14.20.CgThis paper reports unambiguous observationsof the existence of quasistationary states of theneutron in matter. That the effective nuclearscattering potential could lead to such states wasfirst pointed out by Eagan. ' Seregin' subsequent-ly proposed that an arrangement of thin films(with appropriate thickness and made of materi-als having different values of the effective nuclearpotential) could constitute a double-bump potentialbarrier in which neutrons with energies - 10 ' eVcould form quasibound states. The quantum char-acteristics of states in such a potential regioncan be obtained by solving a one-dimensionalSchrodinger equation involving only the neutronwave-vector component, k„perpendicular to thepotential barrier. In semiclassical (WEB) ap-proximation, the values of k, for which suchstates are formed are given byFig. 1, the ultracold neutron beam produced bythe neutron turbine facility' at the Forschungs-reaktor Munich (Garching) is guided (via neutronguides) to the entrance slit system of the gravitydiffractometer. The diffractometer, in brief,consists of entrance and exit slit systems (slitsof 2 cm width together with beam stops) and threeneutron mirrors, two vertical and one horizontal.The entrance and exit slit height corresponds tothe maxima of the neutron flight parabolae for theincoming and exiting beam. In these conditionsthe entrance slit is imaged on the exit slit. Thevertical position of the horizontal mirror (meas-ured from the slit height, or, more precisely,from the center of gravity of the maxima for theset of incident neutron trajectories capable ofpassing the system) measures the fall height, s,of the neutron. The value of k„ then, is given byk, —= (rr/d)(Ii+ s), k, = (m/I)(2')'", (4)where d is the width of the potential well enclosedby the two humps, andn is a positive integer in-cluding 0. Also,k. =[2m(E„-V)]'"/I, (2)where m denotes the neutron mass, E„the kineticenergy corresponding to the neutron velocity com-ponent in z direction, andV =2&SNb/m,the scattering potential at the bottom of the well.N and 5, respectively, are the number density(in inverse cubic centimeters) and the coherent-scattering length of the medium.In the experiment reported here, values of k,could be varied with use of the "gravity diffrac-tometer"' ' for ultracold neutrons. As shown inwhere g is the acceleration due to gravity.In the normal operation of the gravity diffrac-tometer, shown in Fig. 1, the center of the firstvertical mirror, A, was fixed at fall heights be-tween 50 and 60 cm. The height, &, of the hori-zontal mirror, B, was varied. In order to main-tain the focusing condition, the horizontal posi-tion of the second vertical mirror, C, requiresspecific adjustment. The reflected intensity wasmeasured using a BF, detector depleted in "Bcontent and arranged 80 cm below the exit slit.Thus, the neutrons gain enough energy in the gra-vitational field to be able to penetrate the thin de-tector window (0.1 mm Al).A measurement of beam intensity with horizon-tal mirror, B, as nickel-coated glass mirror of10 cm&& 20 cm yielded 45 counts per hour (about1306 1980 The American Physical SocietyVOLUME 44, NUMBER 20 PHYSICAL REVIEW LETTERS 19 MAY 1980Beam StopsMirrorBeam StopsExit SlitMirrorFromNeutron TurbinencIi GuideTubeIlIDetectorMirror Bor ReflectionTargetFIG. j.. Experimental arrangement showing the positions of the multilayered targets. For reflection measure-ments, the target acts as the horizontal mirror, &, of the mirror system of the gravity diffractometer. The en-trance and exit slit (together with beam stops) define and analyze the ultracold neutron beam. A change in the fallheight is achieved by a change in vertical target position.one-half of the value measured previously' ')with a small negative slope (0.18 counts/h cm) athigher values of ~. The dispersion in the valueof k„convoluted with the analyzer (exit) slit reso-lution as determined by the slit width, was meas-ured by varying the vertical exit slit position.The full width at half maximum (FWHM) of theresolution curve determined in this way was 3cm, the same as in Refs. 3 and 4 and consistentwith the value b,k, /k, = zb, ~/z —= l%%uo obtained by aMonte Carlo simulation of neutron passage throughthe instrument. 4The properties of the neutron beam reflectedfrom a double-hump potential barrier were stud-ied by replacing the mirror B by a target of thesame size and consisting of thin films of alumi-num and copper deposited on glass substrate.The double-hump potential well is created bysandwiching an Al film (nominal thickness 860 A)between two Cu films of 240 A each. These filmswere evaporated on the glass substrate one at atime, monitoring the thickness by the frequencyof a quartz crystal. During the evaporation thesubstrate was continuously rotated in such a wayas to limit variations of film thickness over thesample extension to &3%. The outer Cu layer wasprotected from oxidation by an additional 100-A-thick Al film. The total thickness of the layersdetermined by an optical-interference microscopewas found to agree with the quartz-crystal data.The intensity reflected from the target meas-ured as a function of fall height is shown in Fig.2. The data show a clear reflection minimum at~ =108.5 cm. The solid line in Fig. 2 representsthe calculation of the reflected intensity obtainedby solving the Schrodinger equation for the multi-step potential region due to the Al-Cu-Al-Cu-glass media, as depicted in the inset of Fig. 2.A thickness of 881+ 2 A was required for thewidth of the potential well between the two humpsfor n =1 (second level) for the position of the cal-culated minimum to coincide with the observedvalue at 108.5 cm, in reasonable agreement withthe optical microscope and quartz-oscillator dataof 860 A. The fitted value 225+ 5 A for the Cu-film thickness is slightly less than the nominalvalue of 240 A. The observed width (FWHM) of7.5 cm (7.7 neV) corresponds to a lifetime of thestate of the order of 5/I'=2x10 ' s. The depthof the minimum, should reach almost the back-ground level of 12.4+ 0.4 counts/h. There is onlya slight enhancement due to the instrumental res-olution of 2 neV. The observations, however, in-dicate a noticeable gap between the calculatedminimum 13.8+ 0.4 counts/h and the observedvalue 17.4+ 0.7 counts/h. Possible reasons forthis discrepancy are discussed later.A second target with Cu-Al-Cu film thicknesses1307VOLUME 44, NUMBER 20 PHYSICAL REVIEW LETTERS 19 Mwv 1980(r)40-I—Z'.o50n=1J "=ggneV REFERENCEINTENSITY--L~2I ~ ~Cu . Cu .240A 240Ag 20-I—l2.4 90=: 51TIfTlIOO 860A GlassAl AlI 00 I I 0 I 20 I 50FALL HEIGHT (cm)FIG. 2. Reflected intensity measured as a function ofthe fall height for a target with nominal layer thickness-es: Al (100 A), Cu (240 A), Al (860 A), and Cu (240 A).The substrate is glass. Potential functions representingthese layers are shown in the inset. The intensity min-imum at 108.5 cm corresponds to n = 1 (the second sta-tionary state). The solid curve is an exact solution ofthe one-dimensional Schrodinger equation for the multi-step potential representing the target and includes theinstrumental resolution broade ning.selected to allow observation of the third station-ary state (n =2) showed similar reflection charac-teristics.A transmission target was prepared by evapora-tion of Al (110 A), Cu (180 A), Al (1670 A), Cu(180 A), and Al (110 A) on a substrate assembledfrom eight well-polished 5&&5-cm' silicon crys-tals of 0.25-mm thickness. Silicon was chosenbecause of its low absorption cross section andbecause it can be polished well down to sufficient-ly small thicknesses to achieve a transparency of-70'%%uo in the wavelength range investigated. Thistarget was installed 16 cm above mirror B (Fig.1), thus enabling separation of the transmittedand reflected beams. The measured transmis-sion data are shown in Fig. 3. The data show tworesonances (n =1 and n =2). The line positions(74 and 99 cm) and widths (3.4 and 5.9 cm) arefairly well represented by the solid fitted curvefor the following layer thicknesses: central Allayer, 1663+3 A; Cu barriers, 190+ 5 A.. Thestep in the transmission curve at z =85 cm is dueto different optimal settings of mirror A (Fig. 1),and consequently different incident beam intensi-ties, at lower and higher fall heights. As in thereflection measurements, a discrepancy with ex-pectation is observed in the resonance intensity,since the transmission maxima are lower thancalculated.The Breit-Wigner width for the nth quasista-l5-F10POOZ 5-n=iI =" l.8 neVCuISOACu180ASiO. 25m110~ 1670A IIOAAl Al Alfl» 2I "3.0 neVI70I80 90I 1IOO IIOFall height fcm)FIG. 3. Transmission data for a target with nominallayer thicknesses: Al (110 A), Cu (180 A), Al (1670 A),Cu (180 A), and Al (110 A) . The substrate is silicon of0.25-mm thickness. The two resonances observed cor-respond to n =1 and n =2. The data are compared to thesolid curve calculated for a multistep potential.tionary state at E =E„depends upon the probabili-ty, P, of tunneling through a potential barrier.In quasiclassical (WKB) approximation,P = ezp{- 2d, [2m (V~ —E„)]'"/Kj, (5)where V, andd, are the height and width of thebarrier, respectively. For identical barriers de-fining the double hump the resonance lines are ofnearly Lorentzian shape with a FWHM of 2I'*=@&uP/~, where &&a =E„+,-E„.2' ' For instance,for the resonance of Fig. 2 the respective calcu-lated WEB width is 2I'* =2.2 neV. The exacttreatment yields the value 21' =5.1 neV (for thenominal Cu film thickness) which agrees betterwith the measured value 7.7 neV. The differencecan be explained if Cu film thickness is reduced(225 A instead of 240 A). Similar deviations be-tween exact calculation and measurement wereobserved for the other resonances investigated.As noted earlier, the experimental resonanceextrema for all the targets are lower than the cor-responding calculated and resolution broadenedvalues. A poorer resolution than the 2 neV em-ployed in the calculations can explain the differ-ence. However, exit-slit scans at the position ofref lectivity minimum and at the wings yielded aresolution (FWHM) of -3 cm in agreement withthe instrumental resolution. Unequal transparen-cies of the two potential barriers (P„&P~) wouldlead to nonzero ref lectivity minima (and trans-mission maxima & 1), but the data would require-20% deviations between P„and P~ which are un-likely to exist. Departures from the rectangular1308VOLUME 44, +UMBER 20 PHYSICAL REVIEW LETTERS 19 MAY 1980potential shape (due to diffusion mixing at the Al-Cu boundaries) would result in changes of levelposition and width, but not in reduced resonanceamplitudes. Thus, a slight blurring of the poten-tial boundaries by -80 A would eliminate thesmall mismatch (by 2%) of theoretical and experimental level spacings in Fig. 3. A variation inlayer thickness of -3% is, however, insufficientto account for the reduced resonance amplitudes.Microscopic density fluctuations of surface micro-roughness would give rise to disorder scatteringand, consequently, coherent-beam attenuation,similar to "absorption'* (including nuclear cap-ture and thermal inelastic scattering). Calcula-tion shows that an enhancement of "absorption"in pure Al by a factor of -10'-10' could explainthe data, but such strong scattering is unlikely toexist.The optical analog of the double-hump potentialbarrier is the well-known Fabry-Perot interferom-eter. Thus, the present results indicate that aneutron Fabry-Perot interferometer with a reso-lution of 10 ' eV is feasible.The authors are deeply indebted to Mr. Fuhr-mann of Agfa Corporation (Munich) for his expertand timely help in preparation of the targets.Capable and sustained assistance from Mr. Nageland Mr. Schreiber is gratefully acknowledged.One of us (S.S.M.) deeply appreciates the hospi-tality of Professor W. Glaser during his stay atMunich and the travel assistance from the Univer-sity of Rhode Island. This research was support-ed in part by the German Bundesministerium furForschung und Technologie.Yu. Kagan, Pis ma Zh. Eksp. Teor. Fiz. 11, 235(1970) [JETP Lett. 11, 147 (1970)].A. A. Seregin, Zh. Eksp. Teor. Fiz. 73, 1634 (1977)I. Sov. Phys. JETP 46, 859 (1977)].H. Scheckenhofer and A. Steyerl, Phys. Rev. Lett. 39,1310 (1977).H. Scheckenhofer, Dissertation, Technis che Unive r-sitat Munchen, 1979 (unpublished).A. Steyerl, Nucl. Instrum. Methods 125, 461 (1975).A. Steyerl, T. Ebisawa, K.-A. Steinhauser, andM. Utsuro, Neutron optics with simple multilayersystems" (to be published) .High-Energy Photoproduction of the D +P. Avery, J. Wiss, J. Butler, ' G. Gladding, M. C. Goodman ~T. O'Halloran, J. J. Russell, and A. WattenbergUniversity of Illinois, Urbana, Illinois 6'Z8&&andM. Binkley, J. Cumalat, I. Gaines, M. Gormley, R. L. Loveless, ' and J. PeoplesFermi National Accelerator Laboratory, Batavia, 8'linois 60510M. S. Atiya, and S. D. Holmes, B. C. Knapp, W. Lee, and W. J. WisniewskiColumbia University, Negro York, Nets York 10087(Received 28 February 1980)Photoproduction of the D have been observed where the D decays via D' 7r D andthe D decays via K ~+ and K, n+~ . The D +, D mass difference and the D mass ob-served here are in excellent agreement with previous measurements of charmed mesonsproduced in e e annihilations. The photoproduced D and D signals are producednearly equally at the level of about 100 nb/nucleon.PACS numbers: 14.40.Pe, 13.60.KdWe report on the observation of the D*' (D*-)produced in the wideband neutral beam at Fermi-lab. Both this beam and our detector have beendescribed in a previous Letter. ' Our exposureconsisted of approximately 6 &10"photons withan energy greater than 50 GeV incident on a 2-cm-long scintillator target. The particles emerg-ing from these interactions were analyzed by alarge-acceptance magnetic spectrometer system(multiwire proportional chambers) which includestwo multicell Cherenkov counters with pion threh-olds of 6 and 12 GeV, a large lead-glass arrayfor neutral detection, and a hadron calorimeter.The data described here were recorded under a1980 The American Physical Society 1309

Observation of Quasibound States of the Neutron in Matter

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Observation of Quasibound States of the Neutron in Matter

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