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Nuclear spin

Espín Nuclear. Es una práctica común, representar el momento angular total de un núcleo por el símbolo I, y llamarlo espín nuclear. En los electrones de los átomos se hace una clara distinción entre el espín del electrón y el momento angular orbital del electrón, y luego combinarlos para dar el momento angular total.Pero los núcleos, a menudo actúan como si fueran una sola. Spin nucleare e struttura iperfine Struttura degli spettri atomici che deriva dall'esistenza di uno spin e di un momento magnetico del nucleo Nuclear Spin. The nuclear spin is a vector, and its absolute value is I(I+1)h2π, where I is the quantum number of the nuclear spin, simply called nuclear spin. From: Nuclear and Radiochemistry, 2012. Related terms: Proton; Chemical Shift; Hamiltonian; NMR Spectroscopy; Magnetization; Electron Spin

Nuclear spins are actually already naturally protected. The electrons around the nucleus serve as a kind of shield, keeping the radio waves away from the nucleus. This makes it very hard to control, and very slow to act and measure Nuclear Power in Spain (Updated April 2021) Spain has seven nuclear reactors generating about a fifth of its electricity. Its first commercial nuclear power reactor began operating in 1968

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Nuclear Spin and Angular Momentum: Nucleus consists of two kinds of particles - protons and neutrons. They are both spin 1/2 particles and have an intrinsic. Hydrogen nuclei (protons) have magnetic properties, called nuclear spin. They behave like tiny rotating magnets, represented by vectors. The sum of all the tiny magnetic fields of each spin is called net magnetization or macroscopic magnetization. Normally, the direction of these vectors is randomly distributed Description of the Orbital and Spin angular momentum of each nucleon and hence the total nucleus and its contribution to the Nuclear Potential

Predicting Nuclear Spin ( I) 1) Even/Even. Nuclei containing even numbers of both protons and neutrons have I = 0 and therefore cannot undergo NMR. 2) Odd/Odd. Nuclei with odd numbers of both protons and neutrons have spin quantum numbers that are positive integers. 3) All others. The remaining. The nuclear spin state is the orientation of the spin-generated magnetic field relative to an external magnetic field (B0). Think of the nucleus as a top, and the magnetic field orientation as the spin axis

NMR Active Nuclei: nuclear spin quantum number (I) atomic mass and atomic number Number of spin states = 2I + 1 (number of possible energy levels) Even mass nuclei that have even number of neutron have I = 0 (NMR inactive) Even mass nuclei that have odd number of neutrons have an integer spin quantum number (I = 1, 2, 3, etc Figure 1: (Left) Random nuclear spin without an external magnetic field. (Right)Ordered nuclear spin in an external magnetic field. If the ordered nuclei are now subjected to EM radiation of the proper frequency the nuclei aligned with the field will absorb energy and spin-flip to align themselves against the field, a higher energy state The energy difference between nuclear spin states is small compared with the average kinetic energy of room temperature samples, and the +1/2 and _ 1/2 states are nearly equally populated. Indeed, in a field of 2.34 T the excess population of the lower energy state is only six nuclei per million. Although this is a very small difference , when. Nuclear Spin •Some nuclei have Zero spin -12C, 16O: I = 0 •Many important nuclei have I = ½ -1H, 13C, 31P, 15N etc. •Some have larger spins •I= 1: 14N, 2H; I= 3/2: 1B, 7Li, 23Na; I = 3: 10B -if no. of neutrons and no. of protons are both even, then the nucleus has NO spin; I = 0 -If no. of neutrons + protons is odd, then I is half-integer (1/2 Consequently, the electron and nuclear spins are periodically entangled and disentangled at a rate determined by ω0 and ω−. The spin-echo amplitude measures the electron coherence, which is..

Nuclear Spin - an overview ScienceDirect Topic

  1. Therefore, the spin allotropic isomerism of the H 2 molecule originates in the coupling of both rotational state and nuclear spin. It has been argued 10, 11 that at high pressure (P) ortho - and..
  2. Looking for nuclear spin? Find out information about nuclear spin. The total angular momentum of an atomic nucleus, resulting from the coupled spin and orbital angular momenta of its constituent nuclei. Also known as... Explanation of nuclear spin
  3. $\begingroup$ Across the entire periodic table, nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found. Protons and neutrons each have net spins of ½, but this derives from spin interactions among the elementary particles (quarks) of which they are composed
  4. nuclear spin: an intrinsic form of angular momentum possessed by atomic nuclei containing an odd number of nucleons (protons or neutrons)
  5. So spin is a form of intrinsic angular momentum. Elementary particles such as electrons and protons have spin. Particles having a spin quantum number of s = ½ are known as spin-½ particles or fermions, and include electrons, protons and neutrons — the particles of interest in nuclear magnetic resonance (NMR)
  6. Spin dependence of nuclear force is highly non trivial. As an example, exceptional stability of some particular nucleus with nucleon number (also known as magic number) 2, 8, 20, 28, 50, 82, and 126 can be explained by considering the spin-orbit interactions between nucleons.. To see the role of spin dependence, the deuteron nucleus is a good laboratory

NMR - Theory - Chemistry LibreText

The NMR, MRI relevant nuclear spin is the rotational movement of a subatomic particle (proton or neutron) around its axis.Whether a nucleus has an overall spin, depends on its amount of protons and neutrons. Nuclei with an identical number of protons and neutrons cancel out their overall spins. Nuclei with an odd number of protons or an odd number of neutrons or both have an overall spin nuclear spin Hamiltonian is quite complicated. € H ˆ int 0 € H ˆ int 0 € H ˆ int Secular approx. Molecular motion 1. Secular approximation: large B 0 field dominate some of the internal spin interactions. 2. Motional averaging: with rapid molecular tumbling, some interaction terms fluctutate with time and can be replaced by their.

We obtain a compact analytical solution for the nonlinear equation for the nuclear spin dynamics in the central spin box model in the limit of many nuclear spins. The total nuclear spin component along the external magnetic field is conserved and the two perpendicular components precess or oscillate depending on the electron spin polarization, with the frequency, determined by the nuclear spin. Nuclear spins in certain solids couple weakly to their environment, making them attractive candidates for quantum information processing and inertial sensing. When coupled to the spin of an optically-active electron, nuclear spins can be rapidly polarized, controlled and read via lasers and radiofrequency fields. Possessing coherence times of several milliseconds at room temperature, nuclear. spin system will resonate; the spin system absorbs the energy. Following the RF pulse, a signal termed a free induction decay or FID can be detected as a result of the voltage induced in the sample by the energy absorption. Eventually the nuclear spin system relaxes to the thermal equilibrium situation

Nuclear magnetic resonance (NMR) is a spec-troscopic technique that detects the energy ab-sorbed by changes in the nuclear spin state. The application of NMR spectroscopy to the study of proteins and nucleic acids has provided unique in-formation on the dynamics and chemical kinetics of these systems. One important feature of NM Different mechanisms lead to loss of nuclear spin polarization during laser excitation [33, 34]. For instance, under laser illumination, hyperfine-induced electron-nuclear spin flip-flop processes have a dominant effect on the nuclear spin lifetime T 1 when the applied magnetic field is such that the system is close to the excited-state LAC. The nuclear shell model is used to describe the atomic nuclear configuration. This model takes the Pauli exclusion principle into account. In the above tool, one can enter the values the number of protons and neutron present in the nucleus of an atom. The nuclear configuration of the neutron and proton and the nuclear spin from these configurations will be calculated

Structure of the Nucleons - Assignment Point

How is nuclear spin determined? Physics Forum

- The nuclear force does depend on spin, as we will prove in the case of the deuteron. - Experiments can reveal other properties, such as the fact that there is a repulsive term at very short distances and that there is a component that is angular-dependent (the force is then not central and angular momentum is not. J: nuclear spin coupling constant; typically 1-10 Hz. Note: J-coupling is a nuclear-nuclear magnetic dipole coupling, but it does not refer to the direct through-space electrostatic interaction described on the previous page. Instead it is an indirect through-bond spin-spin interaction Elements with either odd mass or odd atomic number have the property of nuclear spin. 5. If an external magnetic field is applied, the number of Powerpoint Templates Page 5 possible orientations calculated by (2I+1). Hydrogen has spin quantum number I=1/2 and possible orientation is (2*1/2+1=2) two +1/2 and -1/2. 6

Spin (physics) - Wikipedi

The nuclear force is dependent on the spin. Here is a video for you! The video describes the nuclear force with examples explaining its properties. What is Radioactivity? Radioactivity is a nuclear process that occurs due to the decay of the nucleus. Radioactivity is based on the law of conservation of charge Nuclear states have an intrinsic spin and a well defined parity, η = ±1, defined by the behaviour of the wavefunction for all the nucleons under reversal of their coordinates with the centre of the nucleus at the origin. 1,−r2 ···− rA) = ηΨ( r1,r2 ··· rA). The spin and parity of nuclear ground states can usually be determined. Measurement of Nuclear Spin G. Breit and I. I. Rabi Phys. Rev. 38, 2082 - Published 1 December 193

Nuclear shell model - Wikipedi

I am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and neutrons separately, I found 3 protons in the $1d_{5/2}$ sub-shell and 4 neutrons in the same $1d_{5/2}$ sub-shell Nuclear spin in an external magnetic field 10:56. Spin and magnetisation 13:32. Chemical shift 18:16. More on chemical shift 19:26. Analysis of proton spectra 5:05. Taught By. Patrick J O'Malley, D.Sc. Reader. Try the Course for Free. Transcript. Explore our Catalog Join for free and get personalized recommendations, updates and offers.. Nuclear spin is the sum of the spin S of all individual nucleons and the relative angular momentum, L. Protons and neutrons are fermions with spin one-half. Like in atoms, the nuclear angular momentum L follows an integer quantum number. The total should therefore be a half integer number if A is odd, an integer if A is even In the deuterium atom ( 2 H ), with one unpaired electron, one unpaired proton, and one unpaired neutron, the total electronic spin = 1/2 and the total nuclear spin = 1. Two or more particles with spins having opposite signs can pair up to eliminate the observable manifestations of spin. An example is helium El espín (del inglés spin 'giro, girar') es una propiedad física de las partículas elementales por el cual tienen un momento angular intrínseco de valor fijo. El espín fue introducido en 1925 por Ralph Kronig e, independientemente, por George Uhlenbeck y Samuel Goudsmit.La otra propiedad intrínseca de las partículas elementales es la carga eléctric

Nuclear Spi

Nuclear magnetic resonance spectroscopy: It is commonly referred to as NMR, and is a technique which exploits the magnetic properties of certain nuclei to study physical, chemical, and biological properties of matter. The most interesting isotope 12C has nuclear spin 0 and does NOT exhibit magnetic resonance. The same goes for 16O and 32 The reason metastable states form is because a larger nuclear spin change is needed in order for them to return to the ground state. High spin change makes the decays forbidden transitions and delays them. Decay half-life is also affected by how much decay energy is available

Nuclear Spin - FutureLear

Spin dependence of nuclear force is highly non trivial. As an example, exceptional stability of some particular nucleus with nucleon number (also known as magic number) 2, 8, 20, 28, 50, 82, and 126 can be explained by considering the spin-orbit interactions between nucleons.. To see the role of spin dependence, the deuteron nucleus is a good laboratory nuclear spin and parity, the magnetic dipole moment and electric quadrupolar moment, and it can even be used to calculate the probability of transitions from one state to another as a result of radioactive decay or nuclear reactions. Fig. 3: Shell Model energy levels (from Krane Fig. 5.6). Left: Calculated energy levels based o Electron spin has only one value (S = ½, always), but nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found across the entire periodic table. ¹H, the nucleus most commonly used for NMR and MRI, has I = ½, the same spin as the single proton of which it is composed Net nuclear spin polarization emerges from the nuclear spin-selective adiabaticity of the MW sweep. Assuming, for concreteness, a low-to-high-frequency sweep, the gap δ E 13 yields an LZ jump probability between branches 1 and 3, p (1 | 3) ≈ exp (− 2 π Ω 2 / ν ˙), [7] where ν ˙ is the frequency sweep rate

The nuclear spin I of the proton is I = 1/2. The gyromagnetic ratio is positive and is given by 2.675222099 10 ( ) 1.0546 10 (1/2) 2.792 5.050951 10 (1/2) 2.792 4 1 1 27 24 s Oe I P N P ℏ ℏ . (NIST, Fundamental Physics constants) Since >0 for proton, the direction of the magnetic moment p is the same as that of the angular momentum (or. NMR depends on the spin of the nucleus under study - the most common is 1H Nuclear spin in an applied magnetic field A magnetic dipole, m, is produced The spin precesses The spin is quantized 1H has a spin quantum number of either +½ (low E) or - ½ (high E) Many nuclei have suitable spin quantum numbers for NMR

II.2. Nuclear Magnetism In quantum mechanics, it is a fact that particles (i.e., electrons, protons, and composite nuclei) possess an in-trinsic quantity of angular momentum known as spin, which cannot quite be understood as any form of classical rotation. The particle's spin angular momentum along any given direction is quantized, andfor a. 3. Nuclear magnetic resonance spectroscopy (NMR) is a powerful analytical technique used to characterize organic molecules by identifying carbon-hydrogen frameworks within molecules. It is a research technique that exploits the magnetic properties of certain atomic nuclei. It determines the physical and chemical properties of atoms or the. Abstract. A theoretical model of the phonon-mediated nuclear spin relaxation in H 2 O trapped by cryomatrices has been established for the first time. In order to test the validity of this model, we measured infrared spectra of H 2 O trapped in solid Ar, which showed absorption peaks due to rovibrational transitions of ortho- and para-H 2 O in the spectral region of the bending vibration Spin-Spin Coupling • Spin-spin or scalar coupling is the result of Fermi contact interaction between electrons in the s orbital of one nucleus and the nuclear spin of a bonded nucleus. • The magnitude of coupling depends on the degree of electron orbital overlap. The s-character of the orbitals relies heavily on the hybridization of the nucle

In the spinning rotor, the slightly heavier UF 6 that contains U-238 will be slightly more compressed along the rim relative to the lighter UF 6 that contains U-235, which would have a relatively greater concentration near the axis. The separation between the two isotopes created by the centrifugal forces is quite small. However, there is a simple way to substantially increase the degree of. We describe a nuclear spin gyroscope based on an alkali-metal--noble-gas comagnetometer. Optically pumped alkali-metal vapor is used to polarize the noble-gas atoms and detect their gyroscopic precession. Spin precession due to magnetic fields as well as their gradients and transients can be cancelled in this arrangement. The sensitivity is enhanced by using a high-density alkali-metal vapor. [en] We present a method for a subsystem-based calculation of indirect nuclear spin-spin coupling tensors within the framework of current-spin-density-functional theory. Our approach is based on the frozen-density embedding scheme within density-functional theory and extends a previously reported subsystem-based approach for the calculation of nuclear magnetic resonance shielding tensors to. The nuclear force depends on spin of electron. There are no easy and simple answers when it comes to questions about the nuclear force. The force between two nucleons is a complicated residual interaction that leaks outside the color confinement walls of the QCD strong interaction. It is best visualized as due to exchanges of quark - antiquark. 1 (I=5/2) could be used as a multilevel nuclear spin qubit, namely qudit (d=6), for quantum information processing (QIP) schemes and provides an example of novel coordination-chemistry-discriminating nuclear spin isotopes. Our results show that the nuclear spin of the lanthanide must be included in the design principles of molecular qubits and.

Fig. 1 Nuclear spin qubit transistor and its detection scheme. (A) Artist's view of a nuclear spin qubit transistor based on a single TbPc 2 molecular magnet.The molecule, consisting of a Tb 3+ ion (pink) sandwiched between two Pc-ligands (white), is coupled to source, drain, and gate (not shown) electrodes. The four anisotropic nuclear spin states of the Tb 3+ (colored circles) can be. Successful acquisition of 73 Ge NMR spectra has also resulted from the use of the Carr-Purcell-Meiboom-Gill (CPMG) sequence [38, 39].This involves a modification of Hahn's spin-echo method [] where a combination of 90- and 180-degree pulses is used with varying intensity and duration.The radiofrequency pulses are kept coherent and a 90-degree phase shift is incorporated into the first pulse This 13 C spin couples to the electron spin via the hyperfine interaction (23, 31): (1) where μ e and μ n are the electron and nuclear magnetic moments, respectively, |ψ e (r j)| 2 is the electron spin density at the site of the nuclear spin, and angle brackets denote an average over the electron wavefunction, ψ e (r) Cualquier átomo con Número atómico o Masa atómica impar tiene spin nuclear y se puede analizar mediante un equipo de resonancia. Podemos pensar que un protón es una esfera con carga positiva. Esa esfera gira respecto a su eje y genera un campo magnético (B) a su alrededor. Una carga que se mueve genera un momento magnético

The phenomenon is known as spin-spin coupling and provides essential information for a skilled NMR technician to interpret a spectrum. Advanced chemistry - spin-spin coupling. In a molecule the nucleus of an atom can induce in the electrons of the chemical bonds attached to it a very weak magnetic moment nuclear spin and the magnetic field is neglected because it is roughly 3 orders of magnitude smaller than all other rel-evant energy scales [37]. The magnetic fields B z and b x are given in units of energy and energy units are chosen such that = 1. The donor ground and first excited states ar Nuclear Magnetic Resonance. When the nuclear magnetic moment associated with a nuclear spin is placed in an external magnetic field, the different spin states are given different magnetic potential energies.In the presence of the static magnetic field which produces a small amount of spin polarization, a radio frequency signal of the proper frequency can induce a transition between spin states Anatomy Ninja is an anatomy game based on medical illustrations, 3D images, radiographs and CT, MRI images, that will help beginners as well as advanced players perfecting their lower and upper limb anatomy knowledge

Dynamic nuclear polarization (DNP) is an important technique that uses polarization transfer from electron to nuclear spins to achieve nuclear hyperpolarization. Combining efficient DNP with optically polarized nitrogen-vacancy (NV) centers offers promising opportunities for novel technological applications, including nanoscale nuclear magnetic resonance spectroscopy of liquids, hyperpolarized. d) Affect the nuclear spin of an atom. Answer: d. Explanation: The amount of energy available in radio frequency radiation is sufficient for affecting the nuclear spin of an atom. It constitute the most fundamental part of spectroscopy. 10. Nuclei having either the number of protons or neutrons as odd have _____ spin. a) Integral spin b) Half. [en] The probabilities of high spin isomer (J ≥ 10) excitation were measured for the odd-odd isotopes 182 Ta, 190 Ir, 194 Ir, 196 Au and 206 Tl in the photonuclear reactions (γ,n) and (γ,p). The activation method was used for the determination of the reaction yields of nuclei in the isomeric and ground states. The calculations of the isomer excitation probabilities on the basis of the. Nuclear spin noise has also been detected by using an optical Faraday rotation in alkali metal vapor . Electron spin noise was detected recently in the context of force-detected magnetic resonance (20, 21). The rms value of the fluctuating magnetic moment, N 1/2.

1 (I=5/2) could be used as a multilevel nuclear spin qubit, namely qudit (d=6), for quantum information processing (QIP) schemes and provides an example of novel coordination‐chemistry‐discriminating nuclear spin isotopes. Our results show that the nuclear spin of the lanthanide must be included in the design principles of molecular qubits. We describe a nuclear spin gyroscope based on an alkali-metal-noble-gas comagnetometer. Optically pumped alkali-metal vapor is used to polarize the noble-gas atoms and detect their gyroscopic precession. Spin precession due to magnetic fields as well as their gradients and transients can be cancelle Nuclear spin I Nuclear spin S Phonons 11 7 6 2 335 44 B0, B1, external fields 1: Zeeman interaction of nuclear spins 2: Direct dipolar spin interaction 3: Indirect spin-spin coupling (J-coupling), nuclear-electron spin coupling (paramagnetic), coupling of nuclear spins with molecular electric field gradients (quadrupolar interaction Nuclear Spin The nucleus is an isolated system and so has a well de nednuclear spin Nuclear spin quantum number J jJj= p J(J + 1) ~ = 1 m J = J; (J 1);:::; J 1; J: Nuclear spin is the sum of theindividual nucleonstotal angular momentum, j i, J~= X i ~j i; ~j i = ~' i + ~s i j j coupling always applies because of strong spin-orbit interaction.

an overall spin. To determine the spin of a given nucleus one can use the following rules: If the number of neutrons and the number of protons are both even, the nucleus has no spin. If the number of neutrons plus the number of protons is odd, then the nucleus has a half-integer spin (i.e. 1/2, 3/2, 5/2) The nuclear spin energy levels of a spin-1/2 nucleus (e.g. 1H or 13C) in a magnetic field. Resonance occurs when the energy separation of the levels, as determined (h/2 ) B0 I Zero field Magnetic field on m = - 1/2 mI = + 1/2 z B0 z. Experiment #2: Nuclear Magnetic Resonance Exp. #2- 1. A spinning charge generates a magnetic field, as shown by the animation on the right. The resulting spin-magnet has a magnetic moment (μ) proportional to the spin.2. In the presence of an external magnetic field (B 0), two spin states exist, +1/2 and -1/2.The magnetic moment of the lower energy +1/2 state is aligned with the external field, but that of the higher energy -1/2 spin state is.

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The nuclear force is thus seen to be spin dependent and this is also evident from the large difference between the neutron scattering cross-sections of ortho- and para-hydrogen. On the assumption of no orbital angular momentum the magnetic moment of the deuteron should just be the sum of the proton and neutron magnetic moments Spin System Simulator - Graphical density matrix treatment of one spin, AX homonuclear and heteronuclear spin systems; NMR Animations: General Animations. Stern-Gerlach Experiment; NMR and the Periodic Table* Nuclear Precession and the Larmor Frequency* Precession of Magnetization in a One-Frequency FI for N=59 (105Pd) observed spin is 5/2 and for N=61 (109Cd) also it is 5/2. though the higher j value state 1g7/2 is first being filled in pairs. in certain regions the deformation of the nuclear shell becomes significant and residual inter nucleon interaction plays a role For example, isotopic spin is used in nuclear physics to represent the two states of a 'nucleon,' the proton and neutron. Similarly, quarks are paired as isospin 'up' and 'down,' which are the. Interaction with nuclear spins. So far, the interaction of the electron spin with the external magnetic field yields an EPR spectrum with one single line which may be broadened due to the g anisotropy. The information content of the EPR spectrum is considerably increased if nuclei with a spin quantum number I > 0 are found in the environment of.

At the same time, the amount of observational data on spin-type ratios in astronomical environments has grown rapidly. The second workshop Nuclear Spin Effects in Astrochemistry will be held in Grenoble, France, May 2-4, 2017 Nuclear-spin-pattern control of electron-spin dynamics in a series of V(IV) complexes C. E. Jackson, C. Lin, S. H. Johnson, J. van Tol and J. M. Zadrozny, Chem. Sci., 2019, 10, 8447 DOI: 10.1039/C9SC02899D This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. You can use material from this article in other publications without requesting further permissions from.

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The principle of nuclear magnetic resonance is based on the spins of atomic nuclei. The magnetic measurements depend upon the spin of unpaired electron whereas nuclear magnetic resonance measures magnetic effect caused by the spin of protons and neutrons. Both these nucleons have intrinsic angular momenta or spins and hence act as elementary. spin Nuclear No Cuántico 1/2 101/2 105/2 1/2 ( I) No. Estados de spin 2 3 02 30 6 2 Números cuánticos de spin de algunos núcleos Elementos con masa impar y/o número atómico impar Tienen la propiedad de spin nuclear. El número de estados de spin es 2I+ 1, donde Ies el número cuántico de spin nuclear spin during the pulse delay 2τ. Since those nuclear spin states remain the same before and after CPMG sequence, we can repetitively map and read out their quantum states with the help of the ancillary electron spin, and realize the single-shot readout of the target nuclear spin. Besides the effect of locking the nuclear spin to th A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3 He, 4 He, and para-H 2. M. P. de Lara-Castells and A. O. Mitrushchenkov, Phys. Chem. Chem. Phys., 2021, 23, 7908 DOI: 10.1039/D0CP05332E This article is licensed under a Creative Commons Attribution 3.0 Unported Licence Nuclear spin diffusion [] plays an essential role in nuclear-magnetization transfer, nuclear spin relaxation, and dynamic nuclear polarization (DNP) in rigid solids composed of spin-active isotopes, where nuclear spins interact magnetically with one another through the dipole-dipole couplings.In the presence of an externally applied magnetic field, the effect of the dipolar interaction.

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