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34-453: The sensitivity of NMR signal detection depends on the gyromagnetic ratio (γ) of the nucleus. In general, the signal intensity produced from a nucleus with a gyromagnetic ratio of γ is proportional to γ because the magnetic moment , the Boltzmann populations, and the nuclear precession frequency all increase in proportion to the gyromagnetic ratio γ. For example, the gyromagnetic ratio of C

68-459: A gyromagnetic factor equal to 2 follows from Dirac's equation, it is a frequent misconception to think that a g -factor 2 is a consequence of relativity; it is not. The factor 2 can be obtained from the linearization of both the Schrödinger equation and the relativistic Klein–Gordon equation (which leads to Dirac's). In both cases a 4- spinor is obtained and for both linearizations the g -factor

102-512: A magnetic field B {\displaystyle \mathbf {B} } is T = m × B . {\displaystyle \,{\boldsymbol {\mathrm {T} }}=\mathbf {m} \times \mathbf {B} \,.} The identity of the functional form of the stationary electric and magnetic fields has led to defining the magnitude of the magnetic dipole moment equally well as m = I π r 2 {\displaystyle m=I\pi r^{2}} , or in

136-762: A magnetic moment resulting from its spin . While an electron's spin is sometimes visualized as a literal rotation about an axis, it cannot be attributed to mass distributed identically to the charge. The above classical relation does not hold, giving the wrong result by the absolute value of the electron's g -factor, which is denoted g e : γ e = − e 2 m e | g e | = g e μ B ℏ , {\displaystyle \gamma _{\mathrm {e} }={\frac {-e}{2m_{\mathrm {e} }}}\,|g_{\mathrm {e} }|={\frac {g_{\mathrm {e} }\mu _{\mathrm {B} }}{\hbar }}\,,} where μ B

170-403: A truly quadratic fermion. Protons , neutrons, and many nuclei carry nuclear spin , which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is: where μ N {\displaystyle \mu _{\mathrm {N} }}

204-854: Is γ e = − 1.760 859 630 23 ( 53 ) × 10 11 r a d ⋅ s − 1 ⋅ T − 1 {\displaystyle \gamma _{\mathrm {e} }=\mathrm {-1.760\,859\,630\,23(53)\times 10^{11}\,rad{\cdot }s^{-1}{\cdot }T^{-1}} } γ e 2 π = − 28 024.951 4242 ( 85 ) M H z ⋅ T − 1 . {\displaystyle {\frac {\gamma _{\mathrm {e} }}{2\pi }}=\mathrm {-28\,024.951\,4242(85)\,MHz{\cdot }T^{-1}} .} The electron g -factor and γ are in excellent agreement with theory; see Precision tests of QED for details. Since

238-520: Is 4 times lower than that of H, so the signal intensity it produces will be 64 times lower than one produced by a proton. However, since noise also increases as the square root of the frequency, the sensitivity is roughly proportional to γ. A C nucleus would be 32 times less sensitive than a proton, and N around 300 times less sensitive. Sensitivity enhancement techniques are therefore desirable when recording an NMR signal from an insensitive nucleus. The sensitivity can be enhanced artificially by increasing

272-468: Is 7.622593285(47) MHz/T. The gyromagnetic ratio of a nucleus plays a role in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). These procedures rely on the fact that bulk magnetization due to nuclear spins precess in a magnetic field at a rate called the Larmor frequency , which is simply the product of the gyromagnetic ratio with the magnetic field strength. With this phenomenon,

306-425: Is a 90° pulse followed by a 180° pulse after a time period τ and is applied on the proton, the sensitive nucleus (designated, perhaps counter-intuitively, as the I spin, while the insensitive nucleus is the S spin; note, however, that the original paper on INEPT used the opposite designations). The first 90° pulse flips the proton magnetization onto the + y axis of the rotating frame and, due to inhomogeneity of

340-411: Is a ratio of a magnetic property (i.e. dipole moment) to a gyric (rotational, from Greek : γύρος , "turn") property (i.e. angular momentum ), it is also, at the same time , a ratio between the angular precession frequency (another gyric property) ω = 2 πf and the magnetic field . The angular precession frequency has an important physical meaning: It is the angular cyclotron frequency ,

374-502: Is by a factor of 1+ K /2. Unlike with NOE, no penalty is incurred by a negative gyromagnetic ratio in INEPT. It is therefore a useful method for enhancing the signal from nuclei with negative gyromagnetic ratio such as N or Si. The N signal may be enhanced by a factor of 10 via INEPT. The pulse sequence of INEPT, as represented in the diagram, can be read as a combination of a spin echo and selective population inversion (SPI). The spin echo

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408-484: Is found to be equal to 2. Therefore, the factor 2 is a consequence of the minimal coupling and of the fact of having the same order of derivatives for space and time. Physical spin- ⁠ 1 / 2 ⁠ particles which cannot be described by the linear gauged Dirac equation satisfy the gauged Klein–Gordon equation extended by the g ⁠ e / 4 ⁠ σ F μν term according to, Here, ⁠ 1 / 2 ⁠ σ and F stand for

442-426: Is its mass. The derivation of this relation is as follows. It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result then follows from an integration . Suppose the ring has radius r , area A = πr , mass m , charge q , and angular momentum L = mvr . Then the magnitude of the magnetic dipole moment is An isolated electron has an angular momentum and

476-458: Is not aligned with its magnetic moment , will precess at a frequency f (measured in hertz ) proportional to the external field: For this reason, values of ⁠ γ / 2 π ⁠ , in units of hertz per tesla (Hz/T), are often quoted instead of γ . The derivation of this ratio is as follows: First we must prove the torque resulting from subjecting a magnetic moment m {\displaystyle \mathbf {m} } to

510-541: Is the Bohr magneton . The gyromagnetic ratio due to electron spin is twice that due to the orbiting of an electron. In the framework of relativistic quantum mechanics, g e = − 2 ( 1 + α 2 π + ⋯ )   , {\displaystyle g_{\mathrm {e} }=-2\left(1+{\frac {\alpha }{\,2\pi \,}}+\cdots \right)~,} where α {\displaystyle \alpha }

544-545: Is the fine-structure constant . Here the small corrections to the relativistic result g = 2 come from the quantum field theory calculations of the anomalous magnetic dipole moment . The electron g -factor is known to twelve decimal places by measuring the electron magnetic moment in a one-electron cyclotron: g e = − 2.002 319 304 361 18 ( 27 ) . {\displaystyle g_{\mathrm {e} }=-2.002\,319\,304\,361\,18(27).} The electron gyromagnetic ratio

578-470: Is the nuclear magneton , and g n {\displaystyle g_{\rm {n}}} is the g -factor of the nucleon or nucleus in question. The ratio γ n 2 π g n , {\displaystyle \,{\frac {\gamma _{n}}{\,2\pi \,g_{\rm {n}}\,}}\,,} equal to μ N / h {\displaystyle \mu _{\mathrm {N} }/h} ,

612-424: Is the population inversion part of the scheme, where a further 90° pulse after a time period on both the sensitive and insensitive nuclei rotate the magnetization onto the z -axis. This has the effect of producing an antiphase alignment of magnetization on the z axis, an important step during which the polarization is transferred from the sensitive nucleus to the insensitive one. There are a number of variations of

646-460: The precession of a gyroscope. The earth's gravitational attraction applies a force or torque to the gyroscope in the vertical direction, and the angular momentum vector along the axis of the gyroscope rotates slowly about a vertical line through the pivot. In place of a gyroscope, imagine a sphere spinning around the axis with its center on the pivot of the gyroscope, and along the axis of the gyroscope two oppositely directed vectors both originated in

680-453: The Boltzmann factors. One method may be through NOE; for example, for C signal, the signal-to-noise ratio can be improved three-fold when the attached protons are saturated. However, for NOE, a negative value of K , the ratio of gyromagnetic ratios of the nuclei, may result in a reduction in signal intensity. SinceN has a negative gyromagnetic ratio, the observed N signal can be near zero if

714-556: The Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while A is the electromagnetic four-potential . An example for such a particle is the spin ⁠ 1 / 2 ⁠ companion to spin ⁠ 3 / 2 ⁠ in the D ⊕ D representation space of the Lorentz group . This particle has been shown to be characterized by g = ⁠− + 2 / 3 ⁠ and consequently to behave as

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748-502: The center of the sphere, upwards J {\displaystyle \mathbf {J} } and downwards m . {\displaystyle \mathbf {m} .} Replace the gravity with a magnetic flux density B   . {\displaystyle \,\mathbf {B} ~.} d ⁡ J d ⁡ t {\displaystyle {\frac {\,\operatorname {d} \mathbf {J} \,}{\,\operatorname {d} t\,}}} represents

782-460: The desired formula comes up. d ^ {\displaystyle {\hat {\mathbf {d} }}} is the unit distance vector. The spinning electron model here is analogous to a gyroscope. For any rotating body the rate of change of the angular momentum J {\displaystyle \,\mathbf {J} \,} equals the applied torque T {\displaystyle \mathbf {T} } : Note as an example

816-476: The dipolar relaxation has to compete with other mechanisms. Alternative methods are therefore necessary for nuclei with a negative gyromagnetic ratio. One such method using the INEPT pulse sequence was proposed by Ray Freeman in 1979, which became widely adopted. The INEPT signal enhancement has two sources: As a result, INEPT can enhance the NMR signal by a factor larger than K , while the maximum enhancement via NOE

850-407: The experiments, for example, a symmetric refocusing step or an extra 90° H pulse may be added, and there are also reverse INEPT pulse sequences. Gyromagnetic ratio In physics , the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum , and it is often denoted by

884-520: The following way, imitating the moment p of an electric dipole: The magnetic dipole can be represented by a needle of a compass with fictitious magnetic charges ± q m {\displaystyle \pm q_{\rm {m}}} on the two poles and vector distance between the poles d {\displaystyle \mathbf {d} } under the influence of the magnetic field of earth B . {\displaystyle \,\mathbf {B} \,.} By classical mechanics

918-452: The laws of classical physics, it has both a magnetic dipole moment due to the movement of charge and an angular momentum due to the movement of mass arising from its rotation. It can be shown that as long as its charge and mass density and flow are distributed identically and rotationally symmetric, its gyromagnetic ratio is where q {\displaystyle {q}} is its charge and m {\displaystyle {m}}

952-419: The linear velocity of the pike of the arrow J {\displaystyle \,\mathbf {J} \,} along a circle whose radius is J sin ⁡ ϕ , {\displaystyle \,J\sin {\phi }\,,} where ϕ {\displaystyle \,\phi \,} is the angle between J {\displaystyle \,\mathbf {J} \,} and

986-455: The same time as the field inhomogeneity, and this property allows the magnetization to be manipulated independent of the chemical shifts. The refocusing allows all the proton chemical shifts to undergo population inversion in the SPI step without its undesirable selectivity. As shown in the diagram, a 180° pulse is applied on the insensitive nucleus simultaneously with the 180° pulse on the proton. This

1020-429: The sign of γ determines the sense (clockwise vs counterclockwise) of precession. Most common nuclei such as H and C have positive gyromagnetic ratios. Approximate values for some common nuclei are given in the table below. Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a nucleus , or an electron , when placed in an external magnetic field B (measured in teslas) that

1054-418: The static magnetic field, the isochromats fan out at slightly different frequencies. After a time period, a 180° pulse is applied along the x axis, rotating the isochromats towards the - y axis. As each individual isochromat still precesses at the same frequency as before, all the isochromats converge and become refocused, thereby regenerating the signal, i.e. the echo. The chemical shifts are also refocused at

Insensitive nuclei enhanced by polarization transfer - Misplaced Pages Continue

1088-466: The symbol γ , gamma. Its SI unit is the radian per second per tesla (rad⋅s ⋅T ) or, equivalently, the coulomb per kilogram (C⋅kg ). The term "gyromagnetic ratio" is often used as a synonym for a different but closely related quantity, the g -factor . The g -factor only differs from the gyromagnetic ratio in being dimensionless . Consider a nonconductive charged body rotating about an axis of symmetry. According to

1122-506: The torque on this needle is T = q m ( d × B ) . {\displaystyle \,{\boldsymbol {\mathrm {T} }}=q_{\rm {m}}(\mathbf {d} \times \mathbf {B} )\,.} But as previously stated q m d = I π r 2 d ^ = m , {\displaystyle \,q_{\rm {m}}\mathbf {d} =I\pi r^{2}{\hat {\mathbf {d} }}=\mathbf {m} \,,} so

1156-433: The vertical. Hence the angular velocity of the rotation of the spin is Consequently, f = γ 2 π B   . q.e.d. {\displaystyle f={\frac {\gamma }{\,2\pi \,}}\,B~.\quad {\text{q.e.d.}}} This relationship also explains an apparent contradiction between the two equivalent terms, gyromagnetic ratio versus magnetogyric ratio: whereas it

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