Measurements of atomic recombination in the HERMES polarized hydrogen and deuterium storage cell target

Nuclear Instruments and Methods in Physics Research A 496 (2003) 263–276

Measurements of atomic recombination in the HERMES polarized hydrogen and deuterium storage cell target C. Baumgartena, B. Brauna,b, G. Courtc, G. Ciullod, P.F. Dalpiazd, A. Golendukhinb,e,1, G. Grawa, W. Haeberlif, M. Henochb, R. Hertenbergera, N. Kochb, H. Kolstera,g,2, P. Lenisad,*, A. Nassb, S.P. Pod’yachevb,h, D. Reggianid, K. Rithb, E. Steffensb, J. Stewartc,i, T. Wisef Sektion Physik, Ludwigs-Maximillians-Universitat 85748 Garching, Germany . Munchen, . b Physikalisches Institut, Universitat 91058 Erlangen, Germany . Erlangen-Nurnberg, . c Physics Department, University of Liverpool, Liverpool L69 7ZE, UK d INFN and Dipartimento di Fisica Universita’ di Ferrara, 44100 Ferrara, Italy e Yerevan Institute, 375036 Yerevan, Armenia f Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA g Nationaal Instituut voor Kernfysica en Hoge-Energiefysica (NIKHEF), 1009 DB Amsterdam, The Netherlands h Institute of Automation and Electrometry of SB RAS, Russia i DESY Zeuthen, 15738 Zeuthen, Germany a

Received 14 May 2002; received in revised form 30 September 2002; accepted 30 September 2002

Abstract The use of storage cells has become a standard technique for internal gas targets in storage rings. In case of polarized hydrogen or deuterium targets, recombination of the atoms occurs during the collisions of the atoms with the walls of the storage cell and may lead to a reduction of the target polarization. In this paper, we present measurements of recombination at the polarized internal hydrogen and deuterium gas target of the HERMES experiment in the years 1997–1999 within a temperature range of 35–250 K: The underlying reaction mechanisms will be discussed with respect to the measured temperature and gas density dependence of surface recombination. Special attention is paid to the influence of water on recombination. These dependencies can be consistently described by a combination of three reaction mechanisms. The first one, dominating at temperatures above 120 K; is an activated Eley–Rideal reaction. A second process dominating below 100 K in case of new storage cells, is interpreted as a tunneling reaction between a physisorbed state and an atom chemically bound on the surface. When the storage cell coating is aged by the influence of the HERA positron beam,

*Corresponding author. Address for correspondence: HERMES-Ferrara, DESY, Notkestr. 85, Hamburg 22647, Germany. E-mail address: [email protected] (P. Lenisa). 1 Current address: ATI Technologies Inc., 55 Commerce Valley Dr. W. Thornhill, Canada ON L3T 7V9. 2 Current address: Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 0168-9002/03/$ - see front matter r 2002 Published by Elsevier Science B.V. PII: S 0 1 6 8 - 9 0 0 2 ( 0 2 ) 0 1 7 5 0 - 3

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the second process is suppressed and a third (weaker) process starts to dominate. This third mechanism is described by Langmuir–Hinshelwood type reactions between physisorbed atoms. r 2002 Published by Elsevier Science B.V. PACS: 29.25.P; 07.77 Keywords: Polarized targets; Detection of atomic beams

1. Introduction The HERMES Experiment [1–3] at the electron/ positron ring of HERA at DESY in Hamburg studies the spin structure of proton and neutron by deep inelastic scattering of polarized electrons from the nucleons of a highly polarized internal hydrogen/deuterium gas target. The polarized hydrogen/deuterium target has been installed in the winter shutdown 1995/1996. It was operated with hydrogen for the years 1996 and 1997 and with deuterium in 1998 until the end of 2000. A Stern–Gerlach atomic beam source (ABS) [4] injects spin-polarized atomic hydrogen or deuterium by means of a feed tube into a thin-walled aluminum storage cell [5]. A sample of the target gas leaves the storage cell via a side tube and is analyzed with a Breit–Rabi type polarimeter (BRP) [6–10] and the target gas analyzer (TGA) [9,10]. The TGA is used to measure the ratio of atoms and molecules leaving the sample tube and consists of a beam chopper and a quadrupole mass spectrometer (QMS). This ratio can be used to calculate the fraction of atoms in the sample beam aTGA : The relation between aTGA and the density weighted average atomic fraction inside the storage cell a is called sampling correction. The calculation of the sampling correction is discussed in detail in Refs. [10,11]. Since the not welldetermined polarization of the molecular fraction from recombination can be a major contribution to the systematic uncertainty of the target polarization, it is therefore of great importance for the quality of the HERMES data to keep the amount of molecules from recombination as small as possible. In this paper, measurements are presented, which have been performed with the TGA between HERA positron fills and far off the

working point of the target ð100 KÞ: The aim of these studies was to understand the driving physical mechanisms of recombination in detail. This is essential for the optimization of the target performance and for the calculation of the sampling correction which differs for a densitydependent and a density-independent recombination process.

2. The experimental setup A schematic diagram of the target, which uses a storage cell to increase the target thickness, is shown in Fig. 1. A beam of hydrogen or deuterium atoms is generated in a dissociator which is part of the ABS. The atoms are electron polarized by means of Stern–Gerlach separation in a sextupole magnet system [12]. The polarization is transferred to the nucleons by the exchange of the population of the hyperfine states using adiabatic high frequency transitions (HFTs). Without the hyperfine transitions 2ð3Þ hyperfine states with mJ ¼ þ12 are able to pass the sextupole system in case of hydrogen (deuterium). Their polarization state can be manipulated by the SFT/WFT transition behind the sextupole system without changing the beam intensity. The transition units between the two sextupole subsystems can be used to remove even more hyperfine states from the atomic beam: Atoms in hyperfine states with mJ ¼ 12; which are defocused by the first sextupole subsystem, are not focused by the second subsystem even if their hyperfine state is changed by one of the HFT units. But atoms that pass the first subsystem in a state with mJ ¼ þ12 can still be defocused with a high efficiency in the second subsystem if their spin state is changed by a HFT

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265

discharge tube collimator 1st sexp. magn. syst. chopper sexp. magn. syst.

SFT nozzle

MFT 2nd sexp. magn. syst.

beam blocker

TGA

detector (QMS)

detector (QMS) SFT / WFT chopper

BRP

ABS

storage cell

MFT SFT beam shutter extension tube

injection tube

B

sample tube HERA beam

Fig. 1. The setup of the HERMES polarized hydrogen/deuterium target. The beam axis of ABS and BRP are tilted by 7301 with respect to the horizontal plane to avoid a direct beam into the BRP. The inlet gives a perspective view of the storage cell.

between the sextupole subsystems. The intensity of the ABS deuterium atomic beam can therefore be reduced by about 28% using one HFT and by about 57% using both HFT units. The beam of nuclear polarized atoms is injected into the center of the thin-walled aluminum storage cell via the injection tube and the atoms then diffuse to the open ends of the cell by means of molecular flow and are removed by a high speed pumping system. The cell is coated with Drifilm [13–16] in order to minimize recombination and depolarization by wall interaction. Drifilm is a hydrophobic siliconbased polymer of high radiation hardness. The principal chemical structure is shown in Fig. 2. A small admixture of oxygen is added into the hydrogen/deuterium inlet to improve the dissociator performance, so that the beam of the ABS has a small contribution of (heavy) water which is also injected into the storage cell. The storage cell is mounted on rails which are cooled within a temperature range of 35–260 K using cold helium gas. A longitudinal magnetic field of 330 mT provides the quantization axis for the spins and inhibits nuclear spin relaxation by decoupling the spins of the nucleus and the electron. A second side tube is connected to the

Fig. 2. Schematic diagram of an ideal Drifilm coating [14,15]. Possible chemical structures of misformed coatings are discussed in the same references. Proper Drifilm coatings are hydrophobic, so that the simplest proof of the quality of a coating is done by testing the adhesion of water drops.

storage cell center to allow for a gas sample to diffuse into TGA and BRP, respectively. During the diffusion process, the polarization can be changed by spin relaxation due to wall and spin exchange collisions and the atomic fraction of the target gas can be reduced by recombination. Due to the low gas density inside the storage cell volume recombination can be neglected. The relative amount of atoms and molecules in the target gas is monitored by the TGA. It consists of a mechanical beam chopper for background subtraction and a QMS that is equipped with a

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channel electron multiplier for single ion detection. Two baffles, one behind the sample tube and a second one in front of the crossed beam ionizer of the TGA, ensure that the atoms of the sample beam cannot hit the inner walls of the ionizer. Otherwise these atoms might recombine and produce a fake molecular beam signal. The BRP uses a sextupole magnet system in combination with a beam blocker to reject hyperfine states with mJ ¼ 12 and to focus hyperfine states with mJ ¼ þ12 into a beam detector identical to the TGA setup. Two HFT units in front of the sextupoles allow one to select other combinations of hyperfine states of the sample beam to transmit the sextupoles. A set of at least 4 (6) beam intensity measurements, each with a different state of the HFT units, is used to calculate the hyperfine population of the hydrogen (deuterium) sample beam. The BRP can also be used to monitor the atomic beam intensity.

3. The recombination probability The following derivation gives a short description of how the measurement of the TGA can be used to obtain the recombination probability gr per wall collision, i.e. the probability for a H or D atom to recombine during a wall collision. This probability in general is an unknown function of temperature, gas density and of the specific surface conditions at the position of the wall collision. Since the surface conditions of the target can be influenced by the HERA beam, gr might also be a function of time. Because gr is typically small ðgr 5102 Þ; the atoms hit the storage cell walls several times before they either recombine or enter the TGA. It is therefore reasonable to describe recombination by an averaged recombination probability which is a function of the storage cell temperature, the gas density and the ‘‘average’’ surface condition only. A detailed description of the diffusion process inside the storage cell by molecular flow is given in Ref. [11]. The probability ra for an atom to survive b wall collisions is for a constant recombination prob-

ability gr given as ra ¼ ð1  gr Þb

ð1Þ

which can be approximated for small gr by ra ¼ egr b :

ð2Þ

If NCAD ðbÞ is the distribution of collision ages (collision age distribution, CAD) in the atomic sample measured by the TGA with Z N N X NCAD ðbÞC NCAD ðbÞ db ¼ 1 ð3Þ 0

b¼0

then the average probability r% a is Z N r% a ¼ NCAD ðbÞ egr b db:

ð4Þ

0

It can be shown [11], that the first order approximation of 1=r% a ðgr Þ around gr ¼ 0 is Z N  1 C1 þ bNCAD ðbÞ db gr r% a ðgr Þ 0 ¼ 1 þ /bSgr

ð5Þ

where /bS is the average collision age of the atoms in the sample. Therefore one may use 1 r* a ðgr Þ ¼ ð6Þ 1 þ /bSgr as a first-order approximation for r% a ðgr Þ: Provided a correct normalization the value of r% a ðgr Þ is identical to the atomic fraction due to recombination as measured by the TGA aTGA [10]. aTGA is r r defined by the ratio of the number of atoms Na detected in the TGA relative to the total flux into the TGA, which is given by the weighted sum of the numbers of detected atoms Na and molecules Nm : Hence r% a can be expressed by Na r% a ¼ aTGA ¼ ð7Þ r Na þ c Nm where c is the weight factor in the order of unity depending on the relative velocities and on the relative sensitivity of the QMS for atoms and molecules. This weight factor is obtained by a measurement of the total flow fTGA fTGA pNa þ cNm aTGA r

ð8Þ

while is changing. Due to mass conservation, the weight factor c has to be chosen such that fTGA ¼ const holds, provided that the output of

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the ABS is also constant [9,10]. The combination of Eqs. (6) and (7) yields: gr C

c Nm : /bS Na

ð9Þ

The average collision age /bS of the TGA gas sample can be obtained by molecular flow simulations [9,10,17,18] and is for the standard HERMES storage cell geometry about 635 collisions. The ABS injects a small amount of undissociated molecules. Additionally molecules from the rest gas, that are produced by recombination outside the storage cell, diffuse back into the cell and contribute to the molecular signal measured in the TGA. Both contributions are subtracted from the molecular beam signal before Eq. (9) is applied. The methods to determine these (small) corrections are described in Refs. [9,10].

4. Measurements of recombination 4.1. General observations It has been observed that accidental losses of the HERA electron/positron beam sometimes coincide with a strong and sudden decrease of the measured atomic fraction aTGA [9,10]. Typically aTGA rer r covers after several hours of ABS operation. It is concluded that the HERA beam has an influence on the storage cell surface and that some kind of aging can be expected due to the HERA beam operation. Water adhesion tests with new and used storage cells demonstrated that the Drifilm coating loses its hydrophobic properties within several weeks of HERA operation. It is therefore important to distinguish the behavior of new and aged storage cells. No changes of aTGA are r observed during a normal HERA fill when the HERA beam is properly tuned [9], hence the recombination probability does not typically change within the duration of a HERA fill (about 12 h) except after the mentioned beam losses. All systematic studies of recombination have been performed between HERA fills in order to make sure that gr is a function of storage cell tempera-

267

ture and target density only while other parameters remain constant. The change of the polarization state of the ; target gas has never been observed to change aTGA r except in coincidence with a change of the ABS beam intensity as it is the case, if the transitions between the sextupoles of the ABS are switched on (see Fig. 1). Hence switching these transitions is a proper method to observe the density dependence of gr even though the polarization is changed at the same time. It has been observed that a warming up of the storage cell above about 140 K after a longer time of operation at 100 K produces a considerable increase in the partial pressure of water in the storage cell which has been measured by the water detected by the TGA as shown in Fig. 3. A fraction of this water represents the usual rest gas in the target chamber, it gets frozen on cold parts of the storage cell, the cooling rails and the helium line when the storage cell is cooled to the usual target operation temperature of about 60–100 K: Another contribution is ballistically injected into the storage cell center by the ABS, since the discharge of the dissociator requires a small admixture of oxygen. Since it is known that new storage cell coatings are hydrophobic (while aged ones are not), only little water adsorption takes place on new storage cells even at low temperatures while the surface of an aged (and cold) storage cell is covered to a large extent by water. Therefore studies of the temperature

Fig. 3. Countrates of mass 18 entering the TGA vs. storage cell temperature measured during a warm up of the target storage cell. At a cell temperature between 140 and 150 K; water starts to evaporate (negative countrates have to be related to the background subtraction and statistical fluctuation).

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Drifilm

1

1

0.9

0.9

0.8

0.8

H þ X2CH3 -H2 þ X2CH2 þ Q

0.7

ð10Þ

is exothermic while H þ H2 O þ Q-H2 þ OH

ð11Þ

is endothermic and hence suppressed at low temperatures. It is assumed that process (10) usually is quickly followed by the process H þ X2CH2 -X2CH3 þ Q

ð12Þ

so that the ‘‘coverage’’ of these ‘‘sites’’ by hydrogen is close to unity. 4.2. Recombination at high temperatures Fig. 4 compares the measured temperature dependence of aTGA and recombination for a r

αrTGA

αrTGA

dependence of recombination with an aged storage cell have been performed without prior warming within the limited range 35–120 K and measurements with new storage cells have been performed prior to HERA beam operation directly after the installation of the cell starting from high temperatures ð250 KÞ: The presence of water is important since water is known to inhibit hydrogen or deuterium recombination. The most likely reason for this is that the chemical binding energy of a hydrogen atom in water ð498 kJ=mol ¼ 5:16 eVÞ is larger than in a hydrogen molecule ð435:99 kJ=mol ¼ 4:52 eVÞ [19]. The bond strength of a hydrogen atom in a methyl group of Drifilm is not exactly known but assumed to be close to the bond strength of H–CH2 SiðCH3 Þ3 which is 415:1 kJ=mol ¼ 4:3 eV [19]. Hence the reaction of a hydrogen atom with

0.7

0.6

0.6

0.5

0.5

0.4

0.4 2

10 T/K

10 T/K 10

1

1 γ

γ

10

-1

10

10

-2

10

10 1

2 100K/T

2

3

-1

-2

1

2 100K/T

3

Fig. 4. Measured temperature dependence of hydrogen recombination. The left (right) graphs show results measured with a new (aged) storage cell. The upper plots show the atomic fraction vs. the storage cell temperature T; the lower plots show the (scaled) recombination probability vs. 100 K=T: The curves on the left have been fitted with Eq. (14). For the measurements on the right, which cover a smaller temperature range, g1r has been replaced by a constant for the fit.

C. Baumgarten et al. / Nuclear Instruments and Methods in Physics Research A 496 (2003) 263–276

1  1: aTGA r

ð13Þ

The data have been fit (solid line), by describing the recombination gr as the sum of two terms represented by g0r and g1r with different temperature dependences:     T1 T2 0 1 gr ðTÞ ¼ gr þ gr ¼ k1 exp þ k2 exp  T T ð14Þ where ki are constants and T is the temperature of the storage cell. The first term can be neglected at high temperatures and will be discussed later. The Boltzmann factor of the second term represents the relative number of atoms that have sufficient thermal energy to overcome the activation barrier for the Eley–Rideal (ER) type reaction (10). A fit of the data shown in the left graphs of Fig. 4 with Eq. (14) results in an activation energy Ea ¼ kb T2 ¼ 31:6 meV for the recombinative abstraction of a bond surface atom by hydrogen, where kb is the Boltzmann constant. An equivalent measurement with deuterium yielded Ea ¼ 68 meV for the abstraction by deuterium [10]. Koleske and Gates measured a similar functional dependence using gaseous atomic hydrogen (deuterium) reacting with chemisorbed deuterium (hydrogen) atoms on a crystal silicon surface. They obtained an activation energy of 25 meV for impinging hydrogen and of 48 meV for deuterium [20]. This process is not density dependent because no thermally activated desorption takes place at these temperatures so that the ‘‘chemisorbed’’ layer is almost completely covered. The fact that the activation energy measured by Koleske and Gates is slightly smaller compared to the HERMES case is likely related to the weaker bond strength of a-Si–H compared to a-C–H.

While the high temperature behavior of recombination can be described by just one term, the low temperature behavior is more involved. As shown in Fig. 4, the low temperature behavior differs significantly between aged and new storage cells. The values for T1 obtained by the fit differ significantly, e.g. T1 ¼ 271:3 K ðT1 ¼ 462:7 KÞ for the new (aged) storage cell. This change of behavior is reproducible and advances smoothly with the age of the storage cell as shown in Fig. 5. Two cells have been used in 1997; both of them showed a similar behavior: Recombination becomes significant below 75 K in case of a fresh Drifilm coating and below 45 K in case of an aged storage cell. In both cases recombination at low temperatures decreases with the time of operation. But if an aged storage cell is warmed up above 140 K so that the water is evaporated and then cooled back to 100 K; the atomic fraction is significantly reduced and it takes several hours for the atomic fraction to recover. This behavior is shown in Fig. 6. Besides the difference in the temperature dependence, also the density dependence of recombination differs between aged and new cells. With new storage cells no density dependence of recombination has ever been measured at the HERMES target. But measurements performed with aged storage cells resulted in a clear evidence for a density-dependent recombination process. Fig. 7 shows a measurement of recombination with

1 0.9 0.8 0.7 0.6 0.5 0.4 30

May 24 Jun 27 Jul 1 40

50 T/K

60

70

αrTGA

/bSgr ¼

4.3. Recombination at low temperatures

αrTGA

new and an aged storage cell. A clear maximum in aTGA ; corresponding to a minimum in the r recombination can be seen for the new cell, while almost no temperature dependence for temperatures higher than 70 K can be seen for an aged, water-covered cell. From Eqs. (6) and (7) the following relation between aTGA and gr can be r derived:

269

1 0.9 0.8 0.7 0.6 0.5 0.4 30

Aug 16 Sep 11 Sep 16 40

50 T/K

60

70

Fig. 5. Measured temperature dependence of hydrogen recombination. The plots show the results of several measurements of the temperature dependence of the atomic fraction for the two different storage cells used in 1997: the first (left) and second (right).

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Fig. 6. Effect of cell heating on recombination. The upper figure shows the cell temperature vs. time and the lower figure the corresponding behavior of the measured atomic fraction aTGA : Other measurements have shown that aTGA remains low after a cell heating if the ABS is not running [9]. The small amount of water injected by the ABS is obviously required to cover the storage cell surface in order to inhibit recombination.

deuterium that supports the density dependence for an aged storage cell. An equivalent measurement with the same (but new) storage cell is shown in Fig. 8 where a density dependence is not visible. The conclusion is that at least two different physical mechanisms are responsible for recombination at low temperatures and that these two mechanisms correspond to two different types of surfaces, a new Drifilm surface and a water-covered Drifilm coating. As already mentioned, a coverage of the surface by water is possible only if the Drifilm coating has been exposed to the HERA beam for some time since a new Drifilm coating is hydrophobic.

5. Theory of physisorption and recombination A comprehensive survey on the knowledge about the physical interaction between gas atoms

and solid surfaces is for example given by Hoinkes [21]. The physisorption potential consists of two parts. An attractive part is caused by van der Waals interaction and a repulsive part by shortrange exchange repulsion due to the Pauli principle. Several mathematical formulas have been used to describe the form of the interaction potential. As a consequence of the well-known Lennard– Jones pair potential [22,23] one obtains the following gas-surface potential [21]       3 1 s 9 s 3 UðzÞ ¼ Em  ð15Þ 2 3 z z where z is the coordinate normal to the surface. The potential has a minimum Em at z ¼ s: Along both of the surface coordinates, the potential follows the periodic structure of the solid as illustrated in the right-side graph in Fig. 9. In case of the non-crystalline Drifilm, the structure of UðxÞ can be less regular but will certainly have

C. Baumgarten et al. / Nuclear Instruments and Methods in Physics Research A 496 (2003) 263–276

given by Hoinkes [21], which makes use of the electronic polarizability a of the adsorbed hydrogen atom and of the optical dielectrical constant e of the surface material:

55

T/K, φTGA /a.u.

50 45 40 35

Em ¼ Ka

30

< b > γr

25 20 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

271

e1 eþ1

ð16Þ

where KC11:2 meV=1025 cm3 is a constant obtained for hydrogen physisorption. With a polarizability of atomic hydrogen of a ¼ 6:66793  1025 cm3 [19] and with e calculated as the square of the optical index of refraction n; given as n ¼ 1:4229 in Ref. [19] for disilane ðC6 H18 Si2 Þ; one obtains Em C25:3 meV 0

2000

4000

6000 8000 time/sec

10000

12000

Fig. 7. Measured density dependence of recombination with an aged storage cell at low storage cell temperatures. The ABS is switched between injection modes with 3 and 1 injected hyperfine states. The upper figure shows the storage cell temperature T (dots) and the total flux fTGA (open and filled circles) measured by the TGA vs. time. The lower figure shows the corresponding values of /bS gr for 3 (1) injected hfs as open (closed) circles.

as an estimation of the upper limit for the binding energy of hydrogen on Drifilm. For the ratio Ej =Eb values between 0.3 and 0.8 have been found in physisorption for several adsorbates and adsorbents [28]. Since the sticking times of physisorbed atoms are small, also the coverage Y of the surface by physisorbed atoms is small. The coverage Y can (for Y51) be expressed by Y ¼ Z0 ats

maxima and minima separated by a typical value of Ej : For Ej oEb the physisorbed atoms will jump from site to site and diffuse along the surface before desorbing back into the gas phase. Ghio et al. determined for graphite the energy levels of physisorbed hydrogen and deuterium atoms by the analysis of atomic beam scattering data. They obtained two energy levels E1 ¼ 31:6 meV and E2 ¼ 15:3 meV for hydrogen and four levels for deuterium with E1 ¼ 35:4 meV up to E4 ¼ 5:9 meV [25]. Other measurements with H and 2 H on LiF and NaF [26] yielded ground state energies of 12?14 meV: Measurements on KCl were performed on a clean and on a water-covered KCl surface. The potential depth was found to be unchanged by the water layer. The lowest energy level (binding energy) was about 30 meV for both hydrogen and deuterium [27]. Measurements on Drifilm are not known, but one may use the semi-empirical formula for the potential depth Em

ð17Þ

ð18Þ

where Z0 is the number of impinging atoms per unit time and unit surface area, a is the area of a surface site and ts is the average sticking time of the physisorbed atom. Z0 is given by rffiffiffiffiffiffiffiffiffi nv% kb T ð19Þ Z0 ¼ ¼ n 4 2pm where n is the density of atoms in the gas phase and v% their average thermal velocity. By thermodynamical considerations, one can show that the average sticking time ts for physisorbed atoms approximately follows the Arrhenius law [10]   Eb ts ¼ t0s exp ð20Þ kb T where Eb is the binding energy of physisorption and the high temperature limit t0s is given by the inverse oscillation frequency n of the physisorbed atom perpendicular to the surface. For a typical energy difference DE between two energy levels of about 4–10 meV [27], one expects an oscillator

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60

T/K, φTGA /a.u.

55 50 45 40 35 30 25

< b > γr

20

1

10

-1

0

2000

4000

6000

8000

10000

12000

14000

16000

time/sec Fig. 8. Measurement of recombination with a new storage cell at low storage cell temperatures. The upper figure shows the storage cell temperature T (dots) and the total flux fTGA (open and filled circles, dots) measured by the TGA vs. time. The ABS is switched between injection modes with 3, 2 and 1 injected hyperfine states. The lower figure shows the corresponding values of /bSgr with the same symbols. No density dependence of recombination is visible in this measurement.

frequency n on the order of n ¼ DE=hC1012 s1 [28,29]. Eq. (20) is commonly used and it is usually assumed, that the average residence time at one surface site tc for a physisorbed atom can also be expressed by this type of equation [29–32]:     1 Ej Ej tc ¼ exp ¼ t0c exp ð21Þ nd kb T kb T where Ej is the activation energy for surface diffusion and nd is the maximum jump frequency which is of the same order of magnitude as n in Eq. (20): nCnd : The average number Nj of visited surface sites of a physisorbed atom then is   ts t0 Eb  Ej Nj ¼ ¼ s0 exp : ð22Þ tc tc kb T Since process (11) is energetically suppressed at low temperatures, it is concluded that recombina-

tion on a water-covered surface proceeds directly between physisorbed atoms by H þ H-H2 þ Q

ð23Þ

according to the Langmuir–Hinselwood mechanism. During a wall collision, the chance for a physisorbed atom to meet another atom for recombination is given by the product of the coverage Y and the number Nj of visited surface sites. Thus the recombination probability per wall collision gdr for process (23) is given by   ðt0 Þ2 2Eb  Ej gdr pYNj ¼ na s0 exp : ð24Þ tc kb T Eq. (24) is a model for a density-dependent recombination process that is increasing with decreasing temperatures. In the next section, a model for a density-independent process will be discussed.

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273

5 0

  mobile  states    localized  states 

U(z,x)/meV

-5

Em

-10

Eb

-15 -20

Ej

-25 -30 -35

3

4

5

6

0

5

z/Å

10

15

x/Å

Fig. 9. Illustration of the potential energy Uðx; zÞ vs. the distance z to the surface (left) and along the surface (right). The energy difference between the lowest localized state and the unbound state is the binding energy Eb : The activation energy for surface jump diffusion is Ej and Em is the maximum depth of the potential [24,21].

5.1. The activation barrier

where the integration has to be taken over the range of x; where V ðxÞ > E: For a typical width of ( V ðxÞ  EC50 meV the potential well of 1–2 A; and m ¼ 1 amu; one obtains Tt C104 –108 ; which is a wide range and covers the HERMES results. The energy of a physisorbed atom should not change significantly with the surface temperature.

A

D

50

G

25 U(z)/meV

The high temperature behavior of recombination, as shown in the left plots of Fig. 4, suggests that there is an activation barrier for reactions between atoms incident from the gas phase and chemisorbed atoms. Therefore the scheme of the surface potential has to be modified as shown in Fig. 10. If the width and height of the activation barrier are small enough, then tunneling reactions between physisorbed atoms and chemisorbed atoms are a reasonable model for density-independent recombination at low temperatures, since the coverage of the layer of ‘‘chemisorbed’’ atoms can be assumed to be close to unity. A survey concerning reaction-rate theories including activated and tunneling processes is given in Ref. [33]. The transmission probability Tt for tunneling of an atom with kinetic energy E through a potential barrier V ðxÞ is approximately given by (see for instance Ref. [34]):  Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Tt Cexp 2 dx 2mðV ðxÞ  EÞ=_2 ð25Þ

75

0 -25

Ea H1

-50

F

Eb

Ekin

E H2

-75

C

-100 -125

B 1.5

2

2.5

3

3.5

4

4.5

5

z/Å Fig. 10. Surface potential scheme for reactions with the surface. The curve DEF represents the physisorption potential for atoms as in Fig. 9. The curve ABGEF is the potential energy curve, if the possibility of chemical reactions with the H/D atoms of the methyl groups of Drifilm are taken into account. The curve ABC represents the potential energy for molecules after the reaction. Ea is the activation energy for ‘‘E–R’’ reactions with atoms impinging from the gas phase of thermal energy E > Ea : Physisorbed atoms, that are sticking at position E, may enter the second potential minimum and thus react with the surface by tunneling as indicated by the arrow. The desorbing molecules have an average additional energy Ekin from the exothermic reaction, indicated by a lowered energy base line at 75 meV:

But the number of ‘‘chances’’ to tunnel through the activation barrier is proportional to the average number Nt of oscillation cycles of the physisorbed atom, so that one obtains with

274

Eq. (20)

C. Baumgarten et al. / Nuclear Instruments and Methods in Physics Research A 496 (2003) 263–276



 Eb Nt ¼ ts n ¼ exp : kb T

ð26Þ

Hence the recombination probability gtr per wall collision by tunneling on surface sites which are not covered by water is given by the product of Tt and Nt :   Eb t gr ¼ Tt Nt ¼ Tt exp : ð27Þ kb T Since Tt is independent of atomic density and its dependence on temperature is weak and negligible compared to the exponential factor, Eq. (27) delivers a model for the density-independent recombination process. If f is the fraction of the storage cell wall area covered by water then one obtains for the total recombination probability gr gr ¼ f gdr þ ð1  f Þgtr þ g1r   ðt0s Þ2 2Eb  Ej ¼ fna 0 exp tc kb T     Eb Ea þ ð1  f ÞTt exp þ k2 exp  : kb T kb T ð28Þ The fraction f depends on temperature, time, the quality of the Drifilm coating and fraction of water coverage. If one assumes f -0 for a new storage cell and f -1 for an aged storage cell, then one may use Eq. (14) to fit the measured data of Fig. 4 and obtains Eb ¼ 271:3 K T1ðaÞ ¼ kb 2Eb  Ej ¼ 462:7 K T1ðbÞ ¼ kb where T1ðaÞ holds for a new and ‘‘clean’’ and T1ðbÞ for an aged and water-covered surface. From this, we obtain Eb ¼ kb T1ðbÞ ¼ 23:4 meV

The results are also in very good agreement with the measured temperature dependence of nuclear spin relaxation performed with the HERMES target polarimeter [6]. For the nuclear spin flip probability gz ; one expects a temperature dependence of the form [10]:   Eb þ Ej ð29Þ gz ¼ g0z exp pts tc : kb T The results of four measurements for different aging of the two used cells, corresponding to different surface conditions, are listed in Table 1. They represent measurements of new and of aged storage cells and show that the binding energy of physisorption is nearly independent of the amount of the surface area covered by water [10]. 5.2. Relevance of the electron spin Since the H2 wavefunction requires antiparallel spins, hydrogen atoms with parallel electron spins should not recombine. If we consider the presence of the electron spin, the probability to recombine should be multiplied by the probability that two atoms have opposite electron spins. With N m ðN k Þ being the number of atoms with electron spin up (down), the polarization of the electrons Pe is Pe ¼

Nm  Nk Nm þ Nk

and the relative probability that two atoms have opposite spins is given by 2

N mN k 1 ¼ ð1  P2e Þ 2 m k 2 ðN þ N Þ

so that the recombination probability has to be multiplied by this factor. These considerations are only relevant, if both partners are physisorbed atoms. But since this type of reaction is significant at very low temperatures only where Pe p0:1; the size of the effect reduces to less than 1% and is negligible for the measurements presented here.

Ej ¼ kb ð2T1ðbÞ  T1ðaÞ Þ ¼ 6:86 meV: The result for the binding energy Eb is only slightly below the expected potential depth Em in Eq. (17) and hence in good agreement with the theory of Hoinkes.

6. Summary and conclusions It has been shown that both the temperature and the density dependence of recombination of

C. Baumgarten et al. / Nuclear Instruments and Methods in Physics Research A 496 (2003) 263–276 Table 1 Results of a fit of Eq. (29) for the 7 temperature scans of 1997, performed with hydrogen [10]. The HERMES storage cell has been exchanged prior to the measurement of August 16 Date

Eb þ Ej (meV)

106  g0z

Mar 10 May 24 Jun 27 Jul 1

29:6570:22 28:9070:22 28:4570:77 28:4570:43

3:5870:16 2:1670:10 1:7470:29 1:7770:15

Aug 16 Sep 11 Sep 16

31:6971:16 31:4470:44 30:0270:30

3:6870:85 2:5570:22 2:6370:17

275

the recombination process. The nuclear polarization of these atoms depends on the circumstances. For the case of the HERMES cell which is Drifilm coated, a measurement of the nuclear polarization of the recombined H atoms, performed at 260 K gives indication that, the surface atoms have nonzero nuclear polarization [35]. Other measurements of the nuclear polarization of molecules created by recombination on copper—recently performed at IUCF—suggest that the nucleons of the chemisorbed atoms are completely depolarized [36].

Acknowledgements atomic hydrogen and deuterium on the Drifilm coated HERMES storage cell are consistent with the presence of three different physical mechanisms. These mechanisms have been identified and discussed. The expected temperature and density dependence has been derived and found to be in agreement with the measurements. The resulting values for the binding energy Eb and the activation energy for surface jump diffusion Ej are in excellent agreement with the theoretical expectation. The sum of both values matches the results of spin relaxation measurements simultaneously performed with the HERMES target polarimeter [10]. The measurements lead to the conclusion that recombination between physisorbed atoms is negligible at the typical target operation temperatures between 60 K (deuterium) and 100 K (hydrogen). Hence recombination at the working point is independent of the gas density since the coverage of the ‘‘chemisorbed’’ layer is close to unity. This is an important point for the investigation of the atomic density distribution along the storage cell axis and for the calculation of the average atomic fraction [11]. Recombination at the HERMES target is independent of the electron spin since in every reaction a chemically bound partner is involved. At lower temperatures where two physisorbed atoms react with each other, spin relaxation processes strongly reduce the polarization of the electrons Pe so that a possible influence of Pe on the recombination process is negligible. The residence time of chemically bound atoms on the surface certainly depends on the strength of

We gratefully acknowledge the DESY management for its support and the DESY staff and the staffs of the collaborating institutions. This work was supported by the German Bundesministerium fur . Bildung, Wissenschaft, Forschung und Technologie (BMBF 056MU22I(1) and 057ER12P(2)); the UK Particle Physics and Astronomy Research Council, the US Department of Energy and the National Science Foundation; the Dutch Foundation for Fundamenteel Onderzoek der Materie (FOM) and the Italian Instituto Nazionale di Fisica Nucleare (INFN).

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