Physics Procedia 51 ( 2014 ) 59 – 62

1875-3892 © 2013 The Authors. Published by Elsevier B.V.Selection and peer-review under responsibility of scientifi c committee of NPPatLPS 2013. doi: 10.1016/j.phpro.2013.12.014

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ESS Science Symposium on Neutron Particle Physics at Long Pulse Spallation Sources, NPPatLPS 2013

Ramsey experiments using neutron beams

Florian M. Piegsa*

ETH Zürich, Institute for Particle Physics, CH-8093 Zürich, Switzerland

Abstract

Ramsey’s technique of separated oscillatory fields adapted to cold neutron beams is a very sensitive method to probe for spin-dependent interactions of neutrons with magnetic and pseudomagnetic fields. In the last couple of years several distinctive experiments using this technique have been performed, e.g. to determine the incoherent neutron scattering length of the deuteron, to perform polarized neutron imaging of magnetic fields and samples, and lately, to search for new light spin-1 bosons. Here, some of these results are reviewed and possible future measurements with respect to a pulsed neutron source are presented. © 2013 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of scientific committee of NPPatLPS 2013.

Keywords: Neutron physics; Ramsey technique; Neutron electric dipole moment; Neutron radiography; Exotic interactions.

Originally introduced as a molecular beam resonance method, Ramsey’s technique of separated oscillatory fields has become a well-established tool in many areas of research [1,2]. The method has been adapted to neutrons in various ways and is sensitive to spin-dependent interactions of the neutron spin (magnetic and pseudomagnetic), which are detected as a spin precession phase shift

Δ� � Δ� · �/ (1)

where ћ is Planck’s constant, T is the time the neutron spin experiences the interaction and ΔE is the Zeeman-like

* Corresponding author. Tel.: +41-44-63-32815 E-mail address: florian.piegsa@phys.ethz.ch

Available online at www.sciencedirect.com

© 2013 The Authors. Published by Elsevier B.V.Selection and peer-review under responsibility of scientific committee of NPPatLPS 2013.

60 Florian M. Piegsa / Physics Procedia 51 ( 2014 ) 59 – 62

energy of the spin state splitting due to the interaction. In a neutron Ramsey experiment, the polarized neutron spins, situated in an external static magnetic field B0, are irradiated with two consecutive phase-locked radio frequency π/2 pulses. A so-called Ramsey oscillation pattern is obtained by scanning the frequency ω of the pulses close to Larmor resonance ω0 = -γn·B0 and determining the resulting spin polarization (γn ≈ -2π × 29.165 MHz/T is the gyromagnetic ratio of the neutron). A spin-dependent interaction applied for the time T between the two pulses induces a corresponding phase shift Δφ of the oscillation pattern. A list of interactions with the corresponding proportionality of ΔE is summarized in Table 1.

Table 1. Spin-dependent interactions of the neutron, where ��n is the magnetic moment, ��

n the electric

dipole moment of the neutron and ��� and ��� are magnetic and electric fields, respectively. Further, ρ is the nuclear number density in a sample with a nuclear spin polarization ���, while � is the neutron velocity, � is the distance vector between the neutron and a nucleon and c is the speed of light in vacuum.

Interaction ΔE � References

Magnetic ��n · ��� [9,12-15]

Neutron electric dipole moment ��n · ��� [8,11] and others

Incoherent scattering length ρ bi ��n · ��� [3-7,16,17]

Exotic interaction (gAgA) ��n · �� �� [20,21]

Exotic interaction (gVgA) ��n · � [21,22]

Axion-like interaction (gSgP) ��n · � [23,24]

Relativistic motional magnetic field ��n · �� ���� / �� [30]

Test of Lorentz invariance [25,26]

Neutron gravitational dipole moment [26,27]

Historically, neutron Ramsey experiments have been performed using beams, for instance to measure the spin-dependent (incoherent) neutron scattering length bi of several nuclei [3-7], to determine the neutron magnetic moment µn and to search for a neutron electric dipole moment dn (nEDM) [8-10]. The latter still represents one of the main applications of Ramsey’s technique, since a non-vanishing value of the nEDM would provide an unambiguous evidence for the breaking of parity (P) and time-reversal symmetry (T). Assuming CPT invariance, a finite nEDM then also implies the violation of the combined symmetry of charge and parity (CP) and new sources of CP-violation are expected to be found to understand the apparent matter-antimatter asymmetry in our universe. Present nEDM experiments, however, prefer using so-called ultracold neutrons, which can be confined in neutron storage bottles with small loss cross sections. This provides much longer interaction times compared to neutron beam experiments and, thus, results in a largely improved sensitivity, with the present best limit of 2.9 × 10-26 e·cm (90% C.L.) [11].

Currently, Ramsey experiments using neutron beams are experiencing a renaissance. For instance, the so-called neutron spin phase imaging technique allows taking quantitative images of magnetic fields and samples [12-15]. Hereby, a two dimensional phase shift map and a neutron attenuation radiography image are obtained simultaneously by means of a position sensitive detector, i.e. a neutron CCD-camera. Another experiment aimed on the precise determination of the incoherent neutron scattering length of the deuteron bi,d by measuring the pseudomagnetic spin precession of polarized cold neutrons passing through a deuterated target containing polarized nuclear spins [16-18]. Combining bi,d with the well-known coherent neutron-deuteron scattering length bc,d [19], provides a value of the doublet neutron-deuteron scattering length b2,d, which represents a crucial input parameter for modern effective field theories of low-energy interactions among nucleons. Moreover, it was demonstrated that, using Ramsey’s technique, one can provide a limit on the strength of the axial-coupling

Florian M. Piegsa / Physics Procedia 51 ( 2014 ) 59 – 62 61

constant for a new light spin-1 exchange boson in the millimeter range. The obtained result limits the axial-coupling constant gA

2 < 6×10-13 (95% C.L.) for an interaction range of 1 mm, i.e. a vector boson mass of about 10-4 eV/c2 [20,21]. An important aspect in these experiments was the use of the two beam method (a Ramsey setup with one beam passing through/by the sample and a second beam serving as a reference), which allows correcting for phase drifts of the Ramsey pattern, e.g. caused by drifts of the magnetic field or of the relative phase between the two π/2 pulses. The method reduces errors due to common noise/drifts and, thus, improves the attainable precision of the phase shift significantly.

All these recent experiments have been carried out at the CW spallation neutron source SINQ at the Paul Scherrer Institute in Switzerland. In principle, they can also be performed at a pulsed spallation source, like the planned European Spallation Source (ESS) in Sweden. In both cases, CW and pulsed sources, one usually limits the neutron wavelength spectrum to a narrow band to avoid a smearing of the Ramsey pattern, i.e. a dephasing of the neutron spins. A Ramsey apparatus installed at a pulsed spallation source, however, could also be operated with a white beam and, thus, profit from a higher neutron flux. This would mainly require that the amplitudes of the radio frequency pulses need to be modulated in time and synchronized with the repetition rate of the spallation source, in order to produce accurate π/2 flips for neutrons of all velocities present in a neutron pulse [28,29]. Such measurements offer the eminent advantage of gathering energy/velocity dependent information in a convenient manner. In the case of a Ramsey experiment this allows for a separation of velocity dependent and independent effects acting on the neutron spin precession frequency. This is of particular interest in the context of a nEDM beam experiment, since it provides the possibility to distinguish between the effect due to a nEDM and the relativistic � � � � - effect. The latter has so far been the limiting systematic effect in nEDM beam experiments [8,10] and can, thus, be overcome by employing a pulsed neutron beam. In such an experiment, an upper limit for a nEDM is determined by comparing the neutron precession frequencies in a constant magnetic field superimposed with an electric field applied parallel and anti-parallel:

�� � ���n · � � � ��n · �� � � �� � � ��/��� (2)

�� � ��n · � � � ��n · �� � � �� � � ��/��� (3)

The difference in precession frequency is given by

Δ� � ��� � ��� � �2��n · � � � 2��n · �� � � ��/�� (4)

Here, the critical assumption is made that the magnetic field does not change during the course of the two measurements. Hence, Eq. (4) yields a velocity dependent phase shift caused by the nEDM and a velocityindependent phase shift due to the relativistic motional magnetic field, since the interaction time T is proportional to the inverse neutron velocity. A detailed description of a proposed new nEDM search using a pulsed neutron beam, including an estimate for the achievable statistical sensitivity and possible systematic effects, is given elsewhere [30].

In conclusion, Ramsey’s method of separated oscillatory fields using neutrons offers a wealth of possibilities in low energy particle physics and polarized neutron radiography. Adapting the technique to a pulsed neutron source allows performing velocity dependent investigations. This might prove beneficial in the search for a nEDM employing a neutron beam.

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